GRECO CLASSIC 0153I
Popular in Course
Popular in Classical Studies
verified elite notetaker
This 83 page Class Notes was uploaded by Hayden Braun on Friday September 4, 2015. The Class Notes belongs to CLASSIC 0153I at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 101 views. For similar materials see /class/177874/classic-0153i-university-of-california-los-angeles in Classical Studies at University of California - Los Angeles.
Reviews for GRECO
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/04/15
Personality and Social Psychology Review 2006 Vol 10 No 1 47766 Copyright 2006 by Lawrence Erlbaum Associates Inc The Paranoid Optimist An Integrative Evolutionary Model of Cognitive Biases Martie G Haselton Communication Studies and Department of Psychology University of California Los Angeles Daniel Nettle Psychology Brain and Behaviour University of Newcastle Human cognition is o en biased from judgments of the time of impact of approach ing objects all the way through to estimations of social outcomes in the future We propose these effects and a host of others may all be understood from an evolution ary psychological perspective In this article we elaborate error management the ory EMT Haselton amp Buss 2000 EMT predicts that if judgments are made under uncertainty and the costs of false positive and false negative errors have been asymmetric over evolutionary history selection should have favored a bias toward making the least costly error This perspective integrates a diverse array of effects under a single explanatory umbrella and it yields new contentspecific predictions Better safe than sorry folk wisdom Nothing ventured nothing gained contradictory folk wisdom These two wisdoms seem contradictory The first urges caution whereas the second reminds us that we have nothing to lose and should throw caution to the wind Yet both seem to capture aspecm of human psy chology A person following both maxims would be a paranoid optimist taking chances in some domains but simultaneously being fearful of certain kinds of harm We argue using insights from signal detection and error management theory EMT that there are good evolutionary reasons why the paranoid optimist mind could evolve Furthermore in which domains it is best to be paranoid and in which to be optimistic is predictable from the pattern of recurrent costs and benefits associated with decisions in that domain throughout our evolutionary history This perspective suggests that one of the curiosities of human cogni We are gmteful to Clark Barrett Daniel Fessler Mark Schaller A 139 A c at ticle and to Karthik Panchanathan and Randolph Nesse for providr ing useful background for the mathematical modeling We thank Dar u v1d for insights on the fundamental attribution error and diseaseravoidr ance phenomena Correspondence should be sent to Martie Haselton University of California Los Angeles Communication Studies and Department of Psychology 3130 Hershey Hall 415 Portola Los Angeles CA 90095 Email haseltonuclaedu tionithe fact that it seems riddled with biasesimay be a functional feature of mechanisms for making judgments and decisions Human cognition has often been shown to be biased Perceivers underestimate the timeto impact of ap proaching sounds Neuhoff 1998 2001 and overesti mate the connection between pictures of snakes and un pleasant outcomes such as electric shocks Tomarken Mineka amp Cook 1989People also appeartohaveava riety of positive illusions Taylor amp Brown 1988 which cause them to overestimate the likelihood that they will succeed in spite of the adversity they face Evi dence in these domains and many others suggests that 1 biases or 1 39 39 adopt one belief on the basis of more slender evidence than would be required to believe in an alternative Until recently many psychologists have been con tent to describe these phenomena their contexts of ap pearance and possible implications without much concern for their ultimate origin As Krebs and Denton 1997 noted in as much as explanation is needed it tends to be proximate in nature Psychologists argue that cognition is performed by a set of simple heuristic procedures which are effective in many circumstances but prone to error in others e g Kahneman Slovic amp Tversky 1982 Miller amp Ross 1975 Or in social do mains biases in judgment serve the proximate function of preserving selfesteem or subjective happiness for the egocentered human animal Crocker amp Park 2003 Greenberg Pyszczynski Solomon amp Pinel 1993 Kunda 1990 Researchers offer evoked biases as examples of just such imperfections q nu a HASELTON AND NETI39LE A noteworthy exception exists in the domain of sex ual inference Haselton and Buss 2000 argued that the documented tendency for men to overestimate women s sexual intent could be an adaptive bias de signed by natural selection Because men s reproduc tion is limited primarily by the number of sexual part ners to whom they gain sexual access a bias that caused men to err on the side of assuming sexual inter est would have resulted in fewer missed sexual oppor tunities and hence greater offspring number than un biased sexual inferences Therefore natural selection should favor sexual overperception in men We further discuss this example later A second example occurs in the perceptual domain Neuhoff 2001 argued that the perceptual bias toward thinking that incoming sources of sound will arrive sooner than they actually do may be adaptive because it is better to be ready too early for an incoming object than too late Here we extend the insight that biased systems can result in higher fitness relative to unbiased ones and demonstrate that a wide variety of biases both positive optimistic and negative paranoid may be brought under a single explanatory umbrella We elaborate EMT Haselton amp Buss 2000 by presenting a mathe matical derivation of the model broadening its poten tial domains of application and presenting new predic tions We argue that a key parameter explaining the direction of biases is the relative effects on fitness of different types of error This effort toward integration is useful because it provides clues about the circumstances in which rea soning in a biased way may have yielded fitness advan tages in the ancestral past thus providing guidance about where we should expect to find the classic bi asesisuch as the fundamental attribution error FAEiand their exceptions and where asyetundis covered biases may be found Equally important this perspective speaks to the ongoing debate about human rationality by demonstrating that biased reasoning need not be deemed a design flaw of human cognition instead it may often be a design feature Error Management and Adaptive Bias Noise and Uncertainty The world of the perceiver is filled with uncertainty ln social inference a judge must overcome the fact that a target s behavior is determined by multiple factors many of which interact in complex ways to produce be havioral outcomes Moreover if the perceiver and tar get are engaged in strategic interaction marked by competing interests important social clues may be concealed or a target might stage interference by en gaging in active deception Social judgment and infer ence may also conceni events that are not directly ob 48 servable because they occurred in the past or might happen in the future These difficulties are not limited to social domains The fact that in complex environments perception is al ways clouded by the presence of confounding noise was central to the development of signal detection the ory in psychophysics Green amp Swets 1966 All forms of judgment under uncertainty will be prone to errors Given the necessary existence of these errors how should systems bestbe designed EMT provides a potential answer EMT EMT Haselton amp Buss 2000 applies the princi ples of signal detection theory Green amp Swets 1966 Swets Dawes amp Monahan 2000 to understanding how natural selection engineers psychological adap tations for judgment under uncertainty In general there are four possible outcomes consequent on a judgment or decision A belief can be adopted when it is in fact true a true positive or TP or it cannot be adopted and not be true a true negative or TN Then there are two possible errors A false positive FP er ror occurs when a person adopts a belief that is not in fact true and a false negative FN occurs when a person fails to adopt a belief that is true The same framework applies to actions An FP occurs when a person does something although it does not produce the anticipated benefit and an EN when a person fails to do something that if done would have provided a benefit The costs of the different outcomes and in particu lar the two types of error are rarely identical In testing hypotheses Type 1 errors FPs are typically consid ered more costly by the scientific community than are Type II errors FNs Thus scientists bias their deci sionmaking systems eg classical inferential statis tics toward making Type II errors because reducing Type 1 errors necessarily increases Type II errors The reverse asymmetry characterizes hazard detection Misses FNs are often much more costly than false alarms FPs This asymmetry holds for humanly engi neered devices such as smoke detectors and for evolved hazard detectors such as anxiety stress and cough Nesse 2001 Thus hazarddetection systems are often biased toward false alarms Whenever the costs of errors are asymmetrical hu manly engineered systems should be biased toward making the less costly error This bias sometimes in creases overall error rates but by minimizing the more costly error it minimizes overall cost Green amp Swets 1966 Swets et al 2000 According to EMT certain decisionmaking adaptations have evolved through natural selection to commit predictable errors When ever there exists a recurrent cost asymmetry between two types of errors over evolutionary time selection PARANOlD OWMISTOGNIHW BIASES will fashion mechanisms biased toward committing er rors that are less costly in reproductive currency Because the human environment is often very un certain and the costs of the two types of errors are likely to be recurrently asymmetric in most fitnessrel evant domains EMT predicts that human psychology contains evolved decision rules biased toward commit ting one type of error over another In the following sections we demonstrate how this model can account for a large number of biases that have been observed empirically First though we derive the central claims of EMT formally using a simple model based on signal detection theory Green amp Swets 1966 Consider the situation where a person might or might not form some belief eg that there is a snake in the grass or that a member of the opposite sex is sexually interested in him The approach can be extended to cover judg ments on a quantitative scale giving essentially the same results but here we consider only cases where there is a dichotomous choice to form a belief or not to do so The belief in question need not be a conscious one By adopting a belie we mean behaving or reason ing as if the corresponding proposition were true Let us call the state of the world that may or may not obtain lowercase s whereas the belief that an individ ual may form is capital S That is to say a person with belief S believes that the world is in state s which may or may not really be the case As detailed previously there are four possible outcomes in such a situation A TP would be where the belief was formed and was in fact true that is S and s A TN would be where the be lief was not formed and was not true S and s An FP would be where the belief was erroneously formed S and s whereas an FN would represent the failure to form a belief that is in fact true S and s The signal detection problem is the problem of how much evidence for the state s to require before adopt ing the belief S For every degree of evidence 8 it is possible to specify the probability of that evidence be ing observed if s or pes and also the probability of that evidence being observed if s or pel s If both pels and pel s are nonzero then there is some un certainty in the world That is the observed evidence could have been generated if the world is in state s or in state s If this uncertainty is not present then the sig nal detection problem is trivial and there is no scope for the evolution of bias according to our formulation lntuitively it would seem that an individual should form the belief S if pels is greater than pel s This is indeed an optimal rule if the a priori probabilities of s and s are equal and the organism s goal is to maxi mize the number of true beliefs Green amp Swets 1966 p 23 The ratio pelspe s is called the likelihood ratio As the likelihood ratio increases the relative probability that s is in fact the case given the observed evidence 8 increases An unbiased decision would mean adopting S wherever the likelihood ratio is greater than 1 Any other threshold is a bias a bias against S if it is greater than 1 and a bias toward S if it is less than 1 From an evolutionary perspective a decision rule is optimal not if it maximizes the number of true beliefs but if it has the best possible effect on the organism s fitness Let us assume that the four possible outcomes have different effects on fitness vTP is the effect on fit ness of believing S when s is in fact the case vTN is the effect of believing S when s is in fact the case vFP is the payoff for a baseless belief S vFN is the effect of believing S when s is actually the case The expected value of any decision is given by the following expression EV 7 pspS I svTP p s I svFN p s p S svTNpS svFP l The burden of expression Equation 1 is simply that the expected value is the sum of the probability of a TP times the payoff for a TP the probability of a TN times the payoff for a TN the probability of an FP times the payoff for an FF and the probability of an FN times the payoff for an EN The optimal decision rule would be one that maximized expression Equation 1 It can be shown that Equation 1 is maximized by adopt ing the belief S wherever the degree of evidence is equal to e where pe s 7 p s39vTNvFP pe us7 ps vTPvFN 2 For economy we do not provide a derivation of this expression in this article but it is given in full in Green and Swets 1966 pp 21723 The lefthand term is the likelihood ratio of 9 given the evidence 8 and the righthand term is made up of the relative frequencies of s and s and the payoffs for the four possible out comes Equation 2 has the satisfying property that if s and s are equally likely a priori and the payoffs for all the possible states are equal then a person should believe S if pels is greater than pel s as intuition would predict The type of case central to this article is that in which the payoffs for the different outcomes are not all equal Although there are four payoffs to consider which can in principle vary independently the situa tion can be made conceptually clearer by holding vTP and vTN constant and equal and defining vFP and vFN as the payoff of the deviation from the optimal out come including opportunity costs caused by the two types of error As long as the errors are measured in re lation to the value of the true outcomes and all payoffs are expressed in the same currency no information is 49 HASELTON AND NETTLE lost by this and it means that only the costs of the two error terms need be considered in making predictions For example in the female investment detection ex ample used in the following the vTP is substantial value of male investment but this may be conceptu alized in terms of vFN as an opportunity cost cost of missing out on male investment thus the model can hold vTP and vTN constant and vary only vFN and vTN without loss of information First consider the case where the cost of an FF is rather small and that of an FN is rather large This would be the situation for example for an animal de tecting a snake The payoff for an FP would be the wasted energy of moving away when in fact there was no danger say 1 unit The payoff for an FN would be allowing a potentially venomous snake too close The negative effect of this could be very large say l to 5 0 units There is some sensory evidence available but that evidence is uncertain For example a stick has many of the properties of a snake The question is how much evidence to require that the perceived object must belong to the class of snakes not the class of sticks before assuming that it is a snake Assume for convenience that ps 01 and p us 09 that is there are nine times as many sticks as snakes in the world This assumption is arbitrary but it affects only the scaling and not the shape of the rela tions to be shown because psp Is is always a con stant Figure 1 plots the optimal point at which the individual should adopt belief S under these condi tions with vFN varying from 1 to 50 When vFN is very small the organism should require a large likeli hood ratio to adopt S because if it does so it incurs the cost of moving away In fact when snakes are rare and not very dangerous there is a bias against detecting them because the optimum threshold is greater than 1 However as vFN increases in magnitude the optimal threshold for adopting S very rapidly declines At vFN 10 the optimal point is at 082 which is a bias to ward detecting snakes At vFN 50 under optimal behavior the individual should adopt S even though s is over five times more likely than s given the evi dence Total costs to fitness are still minimized be cause the rare FN is so much more damaging than even multiple FPs It is far better to see a snake where there is only a stick than vice versa This first example illustrates the smoke detector principle Nesse 2001 2005 if the cost of failing to detect something is relatively high it is best to have a lot of false alarms if it means catching the real event when it does happen Let us also consider another pos sibility Imagine a female trying to detect whether a male is willing to make a significant postreproductive investment if she mates with him The value of this in vestment is positive and an FN involves missing out on it so the opportunity cost vFN is significant let us say 5 However the value of the FF is potentially higher very costly because if she mates and then is deserted Optimum threshold 0 t t t 0 5 1 0 1 5 20 25 30 35 40 45 50 Cost of false negative Figure 1 The optimum threshold likelihood ratio for adopting a belief S Where the cost of the FF is xed at 1 and the cost of the FN varies with the probability of s set at 01 A threshold less than 1 represents a bias toward adopting S For explanations see text 50 PARANOID OPTIMIST COGNITIVE BIASES she faces the possibility of raising an offspring alone and may have trouble finding another partner in future Thus vFP varies from 1 to 50 We assume 40 of all men are deserters Again this is an arbitrary assump tion that affects only the scaling Figure 2 shows the optimum threshold as vFP var ies If the cost of being deserted is low the female should have a bias toward accepting the evidence for male commitment However as the cost of desertion increases the optimum threshold soon exceeds 1 which means that she should not adopt S even when the available evidence is more likely to be have been gen erated by s than 1s If vFP 30 then she should not accept S unless the objective likelihood of s is more than four times that of 1s given the evidence she has been able to observe Thus the model predicts the phe nomenon of commitment skepticism which has been empirically documented by Haselton and Buss 2000 We discuss this example and the research evi dence for it in more detail later The model clearly shows that the optimal decision rule is based not on the objective likelihoods alone but also on the payoffs of the different outcomes EMT as its name suggests deals specifically with the relative costs of the two errors FF and FN but this does not re strict the conclusions that can be drawn because the payoff of a veridical outcome can always be restated as an opportunity cost of the converse error and vice versa The optima generated by a signal detection model will be influenced by the a priori probabilities of the two states of the world and also by how well the ev idence discriminates between the two states that is the distribution of the likelihood ratio However we do not explore those dynamics here see Nesse 2001 2005 for some further exploration of these models in the context of the smoke detector principle also see Swets et al 2000 for applications in diagnostic do mains Our central result is robust to permutations of these other parameters Where the relative costs of the two errors are asymmetric the optimal thresholds are biased away from 1 and toward the less costly error Applications of EMT We review three somewhat overlapping classes of bi ases Our classification system is intended to provide a heuristic organizing scheme rather than an exhaustive mutually exclusive taxonomy We argue that each case is an example of error management The two possible er rors areplausibly asymmetrical in cost and in each case the bias is toward making the less costly error In each case decision makers also face a significant degree of uncertainty about the occurance of an event Protective Effects in Perception Attention and Learning Few failures are as unforgiving as failure to avoid a predator Lima amp Dill 1990 Optimum threshold 0 5 10 15 20 25 30 35 4O 45 50 Cost of false positive Figure 2 The optimum threshold likelihood ratio for adopting a belief S Where the cost of the FN is xed at 5 and the cost of the FP varies with the probability of s set at 06 A threshold greater than 1 represents a bias against adopting S For explanations see text 51 HASELTON AND NETTLE Auditory looming Neuhoff 1998 2001 showed that there are biases in the perception of sounds that are rising and falling in intensity Rising in tensity is usually a cue that the source of the sound is approaching the listener In a series of psychoacoustical experiments involving speakers moving on cables Neuhoff and colleagues demon strate that sounds rising in intensity are perceived as approaching faster than matched sounds that are falling in intensity see Neuhoff 2001 for a review More over they are judged to be closer than equidistant fall ing sounds Neuhoff proposed an adaptive explanation when a source is approaching it is better to be prepared for it too early than too late and so selection would fa vor neural mechanisms that detect approaching sounds in a mariner asymmetric to receding ones This expla nation is compatible with the error management model Natural environments are filled with competing sources of sound that render auditory judgments sus ceptible to error For approaching sounds the rela tively inexpensive FP error would be to take prepara tory action for an arriving sound source too early The FN would be to take such action too late which could well lead to such costly outcomes as being struck by a projectile predator or assailant Thus the optimal sys tem is biased toward FP errors This is the familiar principle of the smoke detector It is better to tune a smoke detector to always detect a genuine fire even if the cost is the occasional false alarm Nesse 2001 2005 also see Bouskila amp Blumstein 1992 We will argue that a whole host of biases fall into this same selfprotective smoke detector class T able 1 Allergy cough and anxiety Nesse 2001 2005 argued for the smoke detector principle in bodily sys tems designed to protect from harm Nesse described medical examples such as allergy and cough where a protective system is often mobilized in the absence of Table 1 Protective Biases in Perception Attention and Learning real threat These defense systems appear to be overresponsive dampening them with drugs or treat ment actually results in few negative effects on the pa tient Nesse 2001 Psychological defense mecha nisms such as anxiety are also easily evoked especially in connection with things likely to have been danger ous in the ancestral environment such as spiders snakes and potentially dangerous persons as we dis cuss later Mirieka 1992 Seligman 1971 Tomarken et al 1989 A tendency for anxiety mechanisms to produce FPs is a plausible explanation for the observed prevalence of phobias and anxiety disorders Nesse 001 Dangerous animals It has long been argued that humans are phylogenetically prepared to produce a fear response to snakes and spiders Seligman 1971 More recent evidence suggests not only a special sensi tivity to acquire fears of these aricestrally dangerous animals but also biases that serve to elicit fear main tain it and express it more often than it is needed Mineka and colleagues demonstrated that snake fear responses are more easily acquired and more difficult to extinguish than fears of other fearrelevant stimuli see Mineka 1992 for a review Even when extinc tion is successful it tends to be shortlived as the fears are easily reacquired Mineka 1992 In experimenm people overestimate the covariation between electric shocks and images of snakes and spiders but do not overestimate the covariation between shock and im ages of flowers or mushrooms or even images of dam aged electrical outlets de Jong amp Merckelbach 1991 Tomarken et al 1989 Tomarken Sutton amp Mineka 1995 The covariation bias effect appears to be stron gest in people with specific animal fears Tomarken et al 1995 but when the fearrelevant stimuli eg snake photos are raised in frequency in an experiment lowfear individuals also exhibit the covariation bias Domain False Positive FP Cost of FF False Negative FN Cost of FN Result Approaching sounds Ready too early Low Struck by source High Auditory looming Bias toward underestimating Dangerous animals Fear harmless snakes Low Fail to fear venomous High Easily elicited fear eg snakes and and spiders snakes and spiders reaction to snakes spiders and spiders Dangerous persons Fear harmless May be low depending Fail to fear truly hostile High Easily elicited fear people on the relationship others andor inferences of dangerousness Food aversions Avoid a food that is Nonzero but usually Eat a fatally toxic food High Avoidance of any food usually harmless not high that may be associated with ickness Diseased persons Avoid a person who May be low depending Become infected Often high Tendency to avoid is not infectious on the relationship persons With physical af ictions 52 PARANOlD OWMISTOGNIHW BIASES effect Tomarken et al 1989 also see deong amp Merckelbach 1991 Once a negative association with snakes and spiders is established in a person s mind the fear response can be evoked by a much briefer pre sentation of the feared image than is required for asso ciations with other stimuli Ohman amp Soares 1993 Thus there appear to be biases in expressing fears of snakes and spiders and the specialized sensitivity that facilitates the acquisition of these fears may also be conceived of as a biasisnake and spider fears are acquired on the basis of slimmer evidence than are fears of other dangerous objects even those that in contemporary terms are much more dangerous such as electrical outlets guns and automobiles In ancestral environmenm the overexpression of fears of snakes and spiders was inconvenient but not overly costly whereas failing to fear truly dangerous animals would have been extremely costly given the presence of se verely venomous snakes and spiders in tropical re gions Bouskila and Blumstein 1992 developed simi lar predictions about estimations of predation hazard in nonhuman animals Dangerous persons It is quite possible that the greatest threat to life in ancestral environments was other people In modern environments from tradi tional societies to industrialized nations groups regu larly wage deadly wars on one another Keeley 1996 young adult men who are at the peak stage of intrasexual conflict commit a disproportionate number of murders and competing reproductive interests re sult in spousal homicide Daly amp Wilson 1988 Thus a parallel analysis to that advanced for dangerous ani mals applies to dangerous persons There is evidence that cues of interpersonal threats also tend to be pro cessed in a biased fashion For example Fox Russo and Dutton 2002 showed that angry faces capture at tention for longer than happy or neutral faces even when participants are trying to ignore them Similarly Pratto and John 1991 found that words describing un desirable traits capture attention for longer and cause more task interference than words describing neutral or positive traits In practice the extremely undesirable traits are things that evoke interpersonal threat or vio lence such as hostile mean and sadistic Thus these effects may result from the operation of a threat detec tion system that is predisposed to bias attention toward ancestrally dangerous stimuli In ancestral environments betweengroup differ ences in appearance and behavior such as tribal mark ers signaled differences in coalition membership in modem environmenm racial and ethnic cues appear to activate the psychology of intergroup conflict Kurzban Tooby amp Cosmides 2001 Sidanius amp Veniegas 2000 The assumptionthat members of one s own racial or ethnic group are more generous and kind Brewer 1979 and less hostile and violent eg Quillian amp Pager 2001 than outgroup members is a bias that can be understood from an error management perspective Inferences about relatively unknown outgroup members are uncertain For ancestral hu mans the costly FNwas to miss aggressive intentions on the part of others whereas the FP of overinferring ag gressiveness was low especially for members of com peting coalitions This asymmetry did not characterize inferences about in group members in which costly withincoalition conflict would have resulted from un warranted inferences of hostility or aggressiveness Consistent with this analysis ambient darknessia cue signaling increased risk of hostility from othersiin creases racial and ethnic stereotypes connoting vio lence but has little effect on other negative stereotypes e g laziness or ignorance Schaller Park amp Faulkner 2003 Schaller Park amp Mueller 2003 Food aversions A single instance of gastero intestinal malaise following ingestion of a particular food is sufficient to induce a strong longlasting avoidance of that food Garcia Ervin amp Koelling 1966 Rozin amp Kalat 1971 These aversions are likely the product of specialized associative biases designed to help organisms avoid ingesting toxins even at the cost of a lost source of calories As with snake fears taste aversions are longlived and hard to extinguish Only taste and smell cues are effective at creating an aversion auditory or visual cues are gen erally ineffective Rozin amp Kalat 1971 And in con trast to other conditioned associations creating the aversion requires only one trial and the delay be tween ingestion and malaise can be quite prolonged Garcia et al 1966 These associative biases charac terize omnivorous animals for whom they would be most beneficial the ability to form conditioned taste aversions is missing in a species that relies on only one food that is always fresh as it is drunk straight from a live host vampire bats Ratcliffe Fenton amp Galef 2003 The ease with which food aversions are acquired and maintained given relatively slim evi dence of their toxicity results in many false alarmsiavoiding foods that are in fact safe Within the EMT framework the FF is the formation of a taste aversion to a food that is normally harmless This has a nontrivial cost because it may mean missing out for an entire lifetime on an available source of nu trition On the other hand this cost is low compared to the cost of eating a potentially fatal toxin or pathogen a mistake one can make only once so the system is biased toward selfprotection rather than calorific maximization Several other food choice phenomena are illustra tive Children who are less able than adulm to detoxify poisonous plant parts tend to avoid leaves and vegeta bles and are notoriously picky about what they eat Cashdan 1998 Pregnant women whose immune 53 HASELTON AND NETI39LE system is suppressed to avoid attacking the fetus de velop a variety of pregnancyspecific food aversions Fessler 2002 As clever experiments by Rozin and colleagues demonstrate even the mere suggestion that a food might be contaminated is sufficient to elicit avoidance or disgust When given a choice between two containers of sugar people opt for the container la beled table sugar over the one marked NOT sodium cyanide even though they had just watched the exper imenter fill both bottles from the same box of Domino sugar Rozin Markwith amp Ross 1990 Likewise people refuse to eat otherwise tasty food products that are presented in the shape of a disgusting substance such as fudge in the shape of dog feces Rozin amp Fallon 1987 Avoiding the ill People may require little evi dence of illness or contamination to avoid someone whereas much stronger evidence is required to warrant the inference that someone is safe or free from disease Kurzban amp Leary 2001 Park Faulkner amp Schaller 2003 For example although people understand that mere contact is insufficient for the transmission of AIDS they physically distance themselves from AIDS victims demonstrate dose insensitivity by expressing discomfort with even 5 min of contact and exhibit backward contagion as evidenced by discomfort with the thought that an item of clothing they once wore would be woni by an AIDS victim in the future Bishop Alva Cantu amp Rittiman 1991 Rozin Markwith amp Nemeroff 1992 As we discuss later in the Discussion section disease avoidance may be broadly overinclusive and people may also treat other disabilities or pheonotypic anomalies eg obesity as if they are produced by contagious disease The error management interpretation of these phenomena is that the cost of FNs failing to avoid someone with a conta gious disease is high whereas the cost of an FP avoiding contact with a noncontagious person is rela tively low so diseaseavoidance mechanisms will be overinclusive and will express many false alarms This may account for the difficulty in reversing stigmas as sociated with both contagious and noncontagious physical afflictions Bishop et al 1991 as compared with more easily manipulated social stigmas such as those surrounding homosexuality Kurzban amp Leary 2001 This form of defense overresponsiveness might also explain the seemingly irrational local panic asso ciated with outbreaks of SARS and mad cow disease in faraway places Biases in Interpersonal Perception Interpersonal perception is notoriously prone to bias and error We propose that many of these docu mented biases can be interpreted within the framework of EMT Table 2 54 The illusion of animacy Guthrie 2001 used error management logic to explain one of the key fea tures of religionianimism He proposed that in am biguous circumstances to falsely assume that an inten tional agent eg another human has caused some event is less costly than to miss this fact Given that agents often have interests that compete with those of the perceiver it is important to have a low threshold for inferring their presence For example if one encoun tered a collection of twigs arranged in an improbably neat array Guthrie proposed that it would be better to entertain the thought that a human or other intentional agent was responsible for the arrangementiand to in crease one s vigilance to the possibility of the agent s presenceithan to casually ignore it Guthrie 2001 and Atran and Norenzayan in press proposed that be lief in gods may be a byproduct of this adaptive bias The proposed animacy bias is consistent with classic laboratory experiments conducted by Heider and Simmel 1944 see also Bloom amp Veres 1999 When participants view moving images of circles and squares they find it difficult not to infer intentional statesgchasing wanting and escaping The tendency to infer intentional states in these stimulus arrays emerges early age 4 and there is preliminary evi dence of crosscultural universality of the bias in Ger mans and Amazonian Indians Barrett Todd Miller amp Blythe 2005 although its magnitude of expression may certainly be variable Common features of reli gion across cultures Atran amp Norenzayan 2004 are also consistent with a universal animacy bias The sinister attribution error overweighting of social gaffes and negative forgiveness bias The sinister attribution error is ego s assumption that rela tively trivial aspects of another s behavior indicate negative thoughts or intentions toward ego Kramer 1994 1998 EMT would predict that such a bias could arise where the costs of failing to detect negative evalu ations that in fact do exist are higher than the cosm of inferring such evaluations where there are none in real ity Kramer has shown that the sinister attribution error and paranoid cognition are exhibited differentially by people under intense scrutiny new to social groups or low in status within an organization see Kramer 1998 for a review also see Fenigstein 1984 In one sinister attribution study 1st and 2ndyear students in a master s program at a prestigious business school were asked how they would interpret ambigu ous interactions with their fellow students They were asked for example what they would infer if they made an urgent phone call the evening before an exam that their fellow student did not retuni or if they were tell ing a joke they thought was funny and one of their fel low students abruptly rose and left the table 1styear students were more likely than 2ndyear students to in terpret the interactions in a personalistic fashion by 55 Table 2 Biases in Sacial and SelfPerceptian Domain Unexplained changes in environment Sinister attribution or response to social scrutiny Dispositio nal inference Cooperation with others Men s perception of Women s sexual interest Women s perception of men s commitment Beliefs in personal control and ef cacy False Positive FP Assume human agency Assume negative evaluation Where there is none Assume negative enduring disposition Believe one can defect or cheat Without negative con sequences Inferring interest Where there is none Inferring Willingness to commit Where there is none Assuming control or ef cacy Where there is none Cost of FF Vigilance against a conspeci c that does not existglow Impairs social networksgcould be signi cant Lost opportunity for social exchangegcould be signi cant 139 h p 39 nen costs of ostmcism are great Wasted courtship effortgrelatively low Desertionghigh Low as long as the costs of trying and failing are low False Negative FN Fail to detect competing or hostile group or individual Fail to detect genuine negative evaluations Fail to detect harmful manipulative dispositions in others r c L e L m coopemte even though one could safely defect or cheat eg Without detection by others Inferring no interest when there is interest Inferring unwillingness to Willingness Assuming inability to control Where control is possible Cost of FN High if insecure or marginal within social network High for certain negative tmits L p 39 when resource amount given is small eg small dollar amount Missed reproductive opportunityghigh Delayed start to y A IoW Passivity and opportunity costsghigh Result llusion of animacy agency bias Paranoid cognition in situations of marginality or low status negative forgiveness bias Fundamental attribution error for uncertain negative traits eg social cheating Social exchange bias tendency to coopemte when defection has greater payoff Overperception of Women s sexual interest by men Underperception of men s commitment by Women Posi ve illusions illusion of control HASELTON AND NETI39LE inferring that their call was not returned because the re cipient did not wish to speak to them or that the person found their joke boring rather than inferring for ex ample that their phone message was never received This effect was amplified when 1styear students imagined that the interaction took place with a 2ndyear student whereas 2ndyear students did not make differing attributions depending on the status of the person they imagined interacting with In a second study with the business students Kramer investigated whether participants in an economic coordination game believed their fellow participants were trying to sabotage them to earn more money Those who be lieved that their reactions in the game revealed mana gerial skill and that they were being videotaped attrib uted a greater desire for sabotage to their fellow students than those who did not believe they were un der scrutiny Kramer 1994 Savitsky Epley and Gilovich 2001 documented re lated effects Participants committed an experimentally induced social gaffeifailing at a simple anagram test or being described in an embarrassing manner In four studies the participants believed that they were judged as less intelligent and less favorable in their general im pression by strangers than they actually were In sum when individuals are new to social groups or feel that they are under scrutiny they become hypervigilant to the negative thoughts intentions or evaluations of others These situations may resemble ancestral environments where failing to detect negative social evaluations was highly costly such as when en tering into a new coalition or moving into a new vil lage Failing to detect negative intentions or evalua tions could result in ostracism or direct aggression and the consequences could literally have been deadly Baumeister amp Leary 1995 In the context of romantic relationships Friesen Fletcher and Overall 2005 found that men and women tended to underestimate the degree to which their partners had forgiven them after a transgression e g insults irtation with others With transgression severity controlled this bias was strongest in partner ships characterized by less relationship satisfaction Thus as the researchers proposed a negative forgive ness bias may help to ensure that transgressions are fully mended or not further exacerbated especially in relationships that are already on the rocks The FAE When interpreting the behavior of oth ers people are prone to making the FAE which is the assumption that a person s behavior corresponds to his or her underlying disposition to a greater extent than is logically warranted eg Andrews 2001 Nisbett Caputo Legant amp Marecek 1973 Ross 1977 The extent to which this bias is expressed varies between collectivist and individualist cultures with members of collectivist cultures tending to qualify dispositional in 56 ferences by referencing the social context to a greater extent than members of individualist cultures Choi Nisbett amp Norenzayan 1999 When situational and dispositional inferences are disentangled however members of both collectivist and individualist cultures tend to display dispositional inferences to the same de gree Norenzayan Choi amp Nisbett 2002 Kurzban and Leary 2001 argued that many of our initial social judgments are designed to help us avoid poor social paitners This is important because humans depend on one another to a great extent but social partners can in flict costs on each otherifor example through aggres sion cheating or exploitation Thus it is plausible to argue that avoiding aggressive immoral or selfish oth ers has been a major selective pressure on human social cognition eg Cosmides 1989 One effect of the FAE is to cause observers to avoid social partners who have once demonstrated some negative social behavior because it entails the assumption that the person is disposed to do the same again on repeat interaction This aspect of the FAE can be interpreted from an error management per spective see Andrews 2001 for this and other com plementary explanations of the various manifestations of the FAE The FN is to assume that a person s be havior is not representative of his or her longterm disposition and thus not take it into account in future interactions The risks of the FN are becoming in volved with a person who could later inflict harm The FF is assuming someone is antisocially disposed because of a behavior which did not in fact represent his or her underlying dispositions but was brought about by a more transient feature of the context The cost of such an FP might be the avoidance of people who would in fact be appropriate social paitners This cost might be significant but often not as high as the cost of being hurt or exploited Several sources of evidence support these ideas A study by Reeder and Spores 1983 demonstrated that people make attributions about morality in an asym metric fashion In the study perceivers inferred that immoral behavior stealing from a charitable fund was caused by immoral dispositions regardless of situa tional inducemenm whether the target s date encour aged the target to steal money or donate money In contrast in the moral behavior condition in which the target donated money to the fund perceivers infer ences depended on situational cues when the target was encouraged to donate money perceivers inferred lower morality in the target than when the target was encouraged to steal Reeder amp Spores 1983 These results suggest that perceivers may be inclined to err on the side of assuming immorality regardless of mitigat ing circumstances inferences of morality on the other hand are more carefully qualified In a similar vein using the lexical decision para digm Ybarra Chan and Park 2001 found that adults PARANOlD OWMISTOGNIHW BIASES were faster to identify trait words connoting interper sonal social costs eg hostile cruel disloyal than words connoting poor skill eg stupid weak clumsy or positive qualities eg honest friendly gentle Ybarra 2002 concluded that people tend to lean toward seeing the bad in others in morality do mains to protect themselves from poor social pan ners The social exchange heuristic Standard eco nomic principles predict that players in the oneshot prisoner s dilemma game should defect rather than co operate If one partner cooperates but the other defects the cooperator suffers a greater loss than if he or she had defected The interaction is not repeated so there is no incentive to signal cooperativeness and experi ments are carefully devised so that there is no informa tion about reputation that might serve to provide clues about the partner s cooperative disposition at the start of the game Yet cooperation often occurs in the oneshot prisoner s dilemma game and in many other games in experimental economics Camerer amp Thaler 1995 Caporael Dawes Orbell amp van der Kragt 1989 Henrich et al 2001 Sally 1995 Yamagishi and colleagues hypothesized that coop eration in oneshot games results from the operation of a social exchange heuristic Yamagishi Terai Kiyonari amp Kanazawa 2005 They proposed that the costs of falsely believing one can defect without neg ative social consequences are often higher than coop erating when one could safely defect This asymme try should hold when the cosm of unneeded cooperation are relatively low eg a low dollar amount is lost or when the social costs of failing to cooperate potential ostracism are high The costs of ostracism may be particularly high in interdependent social contexts in which cooperation is either highly valued or especially necessary And as predicted in Japanese collectivist samples where exchanges are often closed to outsiders cooperation in oneshot ex periments is higher than in the more individualist United States samples Yamagishi Jin amp Kiyonari 1999 We suggest that this bias can be conceptualized as a combination of error management and an artifact of modern living because in ancestral environments the probability of repeated encounters would have been high and social reputation effects especially potent Thus people may be predisposed to expect negative consequences of nonprosocial behavior even when objectively such consequences are unlikely to follow The bias toward prosociality is the subject of compet ing explanations that take quite different explanatory stances Bowles amp Gintis 2002 Henrich amp Boyd 2001 Price Cosmides amp Tooby 2002 and it is as yet unexplored whether these are complementary or com peting accounts to the social exchange heuristic Sexdifferentiated biases in decoding courtship signals To the degree that the problems of judgment and social inference differed for men and women over evolutionary history or were associated with different cost asymmetries for the sexes EMT predicts that bi ases will be sex differentiated Haselton and Buss 2000 hypothesized a number of sexspecific biases in interpersonal perception The reproductive success of males is ultimately lim ited by the number of females with whome they can mate whereas for females there is no fitness return on increasing numbers of mating partners beyond a cer tain point Symons 1979 indeed additional matings may become costly Rice 1996 2000 Thus for males there is a higher cost to missing out on a mating oppor tunity than there is for females For females pregnancy and offspring care require large investments and fit ness is affected by the continued investment of the male Given these asymmetric costs and benefits Haselton and Buss 2000 argued that men would have adaptive cognitive mechanisms designed to avoid missed mating opportunities whereas women would have cognitive mechanisms designed to avoid postreproductive desertion The error management predictions in this case are that men should tend to overestimate the sexual interest of women with whom they interact because the FN missing a sexual possibility that was in fact real is more costly than the FP inferring a sexual interest where there is none A number of empirical studies demonstrate that men do indeed overestimate women s sexual interest In laboratory studies when male part ners in previously unacquainted maleifemale dyads are asked to infer their pan ner s sexual interest they consistently rate it as higher than the female partner s report suggests and higher than the ratings provided by female thirdparty viewers of the interaction Abbey 1982 Saal Johnson amp Weber 1989 A similar effect occurs in studies using photographic stimuli Abbey amp Melby 1986 Maner et al in press videos Johnson Stockdale amp Saal 1991 short vignettes Abbey amp Harnish 1995 ratings of courtship behaviors Haselton amp Buss 2000 and in surveys of naturally occurring misperception events Haselton 2003 More important evidence of sexual overperception does not appear in women Haselton 2003 Haselton amp Buss 2000 Maner et al 2005 For women in considering the commitment inten tions of a potential partner the FN would be to miss signs of a genuine desire to commit The FP on the other hand would be assumption of a willingness to commitwhere in fact there was little or none A woman making this error could be forced to raise a child with out the help of an investing father which in extant tra ditional societies can more than double the risk of off spring death Hurtado amp Hill 1992 This error could also reduce her future mating potential because it de 57 HASELTON AND NETI39LE creases her residual reproductive value Buss 1994 Symons 1979 Thus EMT predicts a bias in women toward underperception of men s commitment inten tions Laboratory studies confirm that in the courtship context women underestimate men s commitment Women infer that potential indicators of men s desire for a committed relationship eg verbal displays of commitment and resource investment indicate less commitment than men report that they intend such dis plays to indicate Haselton amp Buss 2000 The same result appears when comparing women s and men s ratings of athirdparty man s dating behaviors demon strating that the effect is not attributable to a simple selfiother rating difference that might result from par ticipants concenis about selfpresentation Haselton amp Buss 2000 More important evidence of commit ment bias does not appear in men s assessments of women s behaviors Haselton amp Buss 2000 SelfRelated Biases Positive illusions Some of the best known cog nitive biases conceni beliefs about the self and the fu ture People have been shown to have unrealistically positive views of the self unwarranted optimism about the future and to believe that they control the flow of events to a greater extent than is logically warranted These effects were grouped together by Taylor and Brown 1988 in their seminal review and dubbed positive illusions Since the time of the review some debate has arisen about the pancultural status of the positive illusions In particular members of East Asian cultures such as the Japanese and Chinese have some times been found not to selfenhance but rather to selfcriticize Heine Lehman Markus amp Kitayama 1999 Kitayama Markus Mamumoto amp Norasakkunkit 1997 Yik Bond amp Paulhus 1998 On the other hand some investigators have found that both American and Japanese participants selfen hance S edikides Gaerlner amp Toguchi 2003 but do so in differentways The J apanese participanm rated them selves as more positive than the midpoint on collectivistic attributes such as cooperative and re spectful but did not self enhance on individualistic at tributes such as selfrelian and unique S edikides et al 2003 American participants showed the reverse pattern and were actually selfeffacing on the collectivistic traim S edikides et al 2003 The authors interpret this finding in terms of a universal propensity to selfenhancement which is expressed in whatever domain excellence is rewarded in the local context This interpretationwould accordwith the error manage ment account that we develop later which suggests some ways in which cultural differences could emerge We retuni to this issue in the general discussion Taylor and Brown 1988 p 199 offered an expla nation for the prevalence of the positive illusions that 58 tacitly contains an error management argument They argued that positive illusions motivate people to perse vere toward goals that would be beneficial but which have an objectively low probability of success For ex ample HlV positive men who are developing symp toms of AIDS have beliefs about the controllability of the disease that are unrealistic but nonetheless serve to motivate them toward active healthpromoting be haviors Taylor et al 1992 Nettle 2004 provided a more formal evolutionary model of the Taylor and Brown argument Accurately assessing the likelihood of obtaining some outcome in the real world is very dif ficult because situations do not recur with exactly the same parameters The two possible errors will lead to opposite behaviorsian FN to passivity and an FP to oversanguine behavior with projects taken on that do not succeed EMT predicts that if the cost of trying and failing is low relative to the potential benefit of suc ceeding then an illusional positive belief is not just better than an illusional negative one but also better than anunbiasedbelief see Figure 1 and Table 2 This is the smoke detector principle applied to a positive outcome It is better to believe that you can get some thing desirable even if you cannot as long as the cost of the false alarm is low relative to the opportunity cost of missing out on a fitnessenhancing opportunity The EMT approach does indeed seem to account for the domains where the positive illusions occur People have unrealistically positive views of precisely those characteristics of themselves that are desirable or bene ficial Brown 1986 Campbell 1986 and when peo ple judge third parties and thus derive no potential benefit from enhancement the positive bias disappears Campbell 1986 People are unrealistically optimistic about the probability that fitnessenhancing outcomes such as finding an ideal partner and gaining profes sional status will happen to them Weinstein 1980 People also tend to be unrealistically optimistic about health problemsithat is to underestimate their likeli hood Weinstein 1982 This at first would seem the opposite of what an error management account would predict however our interpretation of this phenome non is that people are unrealistically optimistic about the effectiveness of their own efforts to avoid health problems Taylor Helgeson Reed amp Skokan 1991 Taylor et al 1992 This makes sense from the EMT perspective as trying to avoid health difficulties that are inevitable is a lower cost error than failing to avoid those that are avoidable The two different smoke detector biases predicted by EMTgexcessive sensitivity to potential harms coming from oumide and excessive optimism about benefits that can be obtained by the selfipredict that reasoning in domains controlled by the self may dis play different biases to reasoning in domains beyond the self s control This is the essence of the paranoid optimism phenomenon predicting paranoia about the PARANOlD OWMISTOGNIHW BIASES environment but optimism about the self There are phenomena in the literature that suggest such double standards For example a metaanalysis of over 70 lifesatisfaction studies from nine countries shows that people tend to believe that their own life is getting better although also believing that life in general in the country where they live is getting worse Hagerty 2003 Similarly people feel they are less likely than average to be involved in an automobile accident when they are the driver but not when they are the passenger McKenna 1993 Such discrepancies are an area where EMT makes interesting predictions for further research For a related arguement in the domain of warfare see Johnson 2004 The illusion of control Finally where events display some randomness people judge that their be havior has a greater in uence on the ow of events than is in fact warranted resulting in the illusion of control Alloy amp Abramson 1979 Langer 1975 Langer amp Roth 1975 Rudski 2000 Vazquez 1987 Given that the controlling behaviors in these experi ments are usually rather low cost pressing a key for example it is a less costly error to continue the control behavior when it is in fact ineffective the FP than it is to miss out on the chance to control events the FN Related to the illusion of control are superstitions It was Skinner 1948 who first showed that if a pi geon is given food reinforcement every 15 sec re gardless of its behavior it may develop behavioral rit uals such as walking in a circle or rubbing its face on the floor Skinner s explanation was in terms of ad ventitious reinforcement a behavior that had once oc curred before the delivery of food was assumed to have caused the delivery of food Very similar effects can be demonstrated in humans who when presented with actually random pattenis of reinforcement de velop superstitious beliefs about actions they must perform to produce the desired contingency Catania amp Cutts 1963 Matute 1994 1995 Ono 1987 Rudski 2001 Such effects are not confined to the laboratory naturalistic surveys reveal that belief in lucky charms and lucky tricks is widespread Vyse 1997 Experimenm by Matute 1994 1995 showed that the result of uncontrollable reinforcement in a human conditioning paradigm is not passivity or learned helplessness but instead superstitious behav ior and a strong subjective illusion of control Only when explicit feedback of the noneffectiveness of the superstitious behavior is provided does the illusion disappear and under such conditions learned help lessness ensues There is a conceptual link with de pression here because depression has often been ex plained in terms of learned helplessness eg Abramson Seligman amp Teasdale 1978 and de pressed participants are distinguished by the absence of illusion in control paradigms Alloy amp Abramson 1979 Vazquez 1987 Thus the evidence suggests that superstitions and illusion of control although strictly speaking irrational are healthy responses to an uncertain world In the ancestral environment accurate information about the true contingencies between people s behav ior and events around them such as the movements of game animals would have been scarce As long as the cost of performing the superstitious behaviors was low relative to the benefit of actually controlling events EMT would predict cognitive mechanisms biased to ward superstition and the illusion of control to evolve Discussion Adaptive Biases We have reviewed a large number of cases where apparently irrational biases in cognition are explained by the existence of asymmetric error cosm and signif icant uncertainty Thus bias in cognition is no longer a shortcoming in rational behavior but an adaptation of behavior to a complex uncertain world Biased mechanisms are not design defects of the human mind but rather design features In view of the con tent specificity of these effects and the absence of bias in many other types of cognition a theory that held bias to be a generalized outcome of individual or cultural learning seems implausible Rather it seems likely that the mind is equipped with multiple do mainspecific cognitive mechanisms with specific bi ases appropriate to the content of the task and the particular patteni of cosm benefits and likelihoods For example we are predisposed to fear spiders and snakes rather than elements of our contemporary en vironment that are in fact much more dangerous such as electrical outlets We are predisposed to fear in jured or diseased people and contamination of the food supply when in fact road traffic and obesity are much more likely to kill us We are prone to sex dif ferences in the perception of sexual intent and to as sume social nonreciprocation has dispositional rather than situational causes We are prone to believe that random events in the environment reflect the opera tions of some unseen intelligence The existence of these biased systems is an impor tant link between psychology and culture To persist in a culture a patteni of information must capture the at tention of individuals such that they will remember and pass it on Those elements of culture best able to ex ploit the inherent biases of the mind will have the greatest probability of being retained and transmitted In fact tales of invisible gods who orchestrate the natu ral world legends of dangerous serpents stories of plagues and taboos about meat all abound in the 59 HASELTON AND NETI39LE world s cultures Atran 2002 Atran amp Norenzayan in press Fessler 2002 Guthrie 2001 Open Versus Closed Developmental Systems Our argument is not that all of the biases we have described are produced by the same cognitive mecha nism but rather that they have all been produced by the same evolutionary mechanismithat is selection to minimize overall error costs acting on many different cognitive systems Some of these systems are rela tively closed For example the system of food aver sions or the predisposition to fear snakes and spiders seems to have fixed content and require only triggering by the environment Other biases such as optimism about future fitness prospects are much more open to environmental influence In one culture the relevant domain for positive illusions might be hunting in an other success in college and in still another standing in the local community The cognitive system leaves open the exibility for the individual to identify those domains in the environment where success yields ben efits and those where failure is costly We would predict that biases produced by relatively closed systems such as snake and spider fears and food aversions would show less crosscultural varia tion Biases such as the positive illusions which are produced by open systems would have the possibility of local variation Such variation might arise for sev eral reasons It might be that in a collective cultural context in which social rewards are contingent on co operation and loyalty to the group the benefits of for example earning extra money are diminished In as much as such cultures disfavor individualists there might actually be significant social costs to individual success in competitive affairs In such a culture the costs of the two errors would actually be different com pared to an individualistic culture and so EMT would predict that positive biases would not appear Indeed EMT would predict that if it is true that East Asian cul tures operate in a more collectivist way than Western ones then the positive biases should be shifted in East Asia toward attributes related to excellence as a collec tive member and away from those to do with excel lence in interindividual competition This is precisely the pattern found by Sedikides et al 2003 Differential Evocation of Bias In many domains ancestrally asymmetries in costs varied depending on context The costs of missing threats are highest for example when individuals are vulnerableiwhen they are sick alone or otherwise unprotected If moderating contexts were recurrent consistent in their effects and signaled by reliable 60 cues we should expect judgmental adaptations to re spond to them with variable degrees of bias We have already discussed several cases in which biases differ by context Sinister attributions are more likely when people are new to social groups negative forgiveness bias is more common in relationships at risk and aggressive stereotypes about outgroups are enhanced in the dark In each of these cases a cue that was present in both ancestral environments and to dayinew social partners relationship discord and darknessishifm the bias A complementary way to understand how adjust ments of bias may occur is through emotion Emotion states are activated in response to threats and opportu nities and they may adaptively channel us toward the specific thoughts and courses of action needed to re spond to them Cosmides amp Tooby 2000 Maner and colleagues Maner et al 2005 hypothesized that fear would increase biases toward inferring aggressiveness in others particularly members of coalitional outgroups sexual arousal on the other hand would in crease men s bias toward overinferring sexual desire in women They showed men and women clips of scary or romantically arousing films and then asked them to in terpret microexpressions in photographs of people who had relived an emotionally arousing experience but were attempting to conceal any facial expressions that would reveal it the faces were actually neutral in expression In the fear condition the study partici pants who were mostly White saw more anger on male faces especially the faces of outgroup Black and Arab males The fear manipulation had no effect on perceptions of sexual arousal in the faces In the ro mantically arousing film condition men perceived greater sexual arousal in female faces particularly when the faces were attractive The arousal manipula tion did not increase men s perceptions of sexual arousal in other men s faces and the manipulation did not increase women s perceptions of sexual arousal in any of the faces Thus the effects were emotion and target specific and for sexual arousal sex specific When fearful men and women perceived greater threat from ethnic outgroup members when aroused men but not women perceived greater arousal in attractive oppositesex faces Park Schaller and colleagues documented parallel effects in the domain of disease avoidance They pro posed that adaptations for disease avoidance are overinclusive and respond to noncommunicable phenotypic anomalies and even a target s status as a foreigner They demonstrated that biased associa tions of phenotypic cues with disease increases when people are fearful of contamination European Ameri can students who read a news clip about a local hepati tis outbreak showed stronger associations between words such as disability and disease and between disability and unpleasant on the implicit associa PARANOlD OWMISTOGNIHW BIASES tion test as compared with controls Park et al 2003 In a subsequent study using the implicit association test participants were exposed to slides evoking patho gen risk germs lurking in a kitchen sponge or acci dents electrocution in a bathtub Those who viewed the pathogen slides showed greater associations be tween slides of obese people and disease than those in the accident condition Park Schaller amp Crandall 2004 Using related methods the researchers found similar effects concerning immigrant groups that were unfamiliar to their Canadian participants Participants in the pathogen condition had more negative attitudes about allowing immigration of unfamiliar immigrant groups Nigerians in one study and Mongolians in an other than familiar immigrant groups Scots and Tai wanese In the accident condition attitudes about these immigrant groups did not differ Faulkner Schaller Park amp Duncan 2004 According to the logic of these studies individuals whose immune sys tems are depressed might also be expected to show in creased bias toward these groups Pregnant women ex perience reproductive immunosuppression to prevent rejection of the fetus which shares only 50 of the mother s genes Fessler 2002 therefore we predict that pregnant women will experience enhanced dis easeavoidance biases Some emotional and motivational states are chroni cally present in some people and therefore biases moderated by these states will also reliably differ be tween them In the microexpressions studies Maner et al 2005 people who believed in general that the world is a dangerous place saw more anger in male outgroup faces People who tended toward a more pro miscuous mating strategy saw more sexual arousal in oppositesex faces Maner et al 2005 In the dis easeavoidance studies individuals who scored high on an individual difference measure of germ aversion or vulnerability to disease also showed stronger dis abilityidisease associations on the implicit attitudes measure Park et al 2003 greater dislike of fat people Park et al 2005 and more negative attitudes about unfamiliar immigrant groups Faulkner et al in 2004 New Predictions EMT predicts the evolution of biases wherever the problem in question involves significant uncertainty has recurred and impacted fitness over evolutionary time and where the two types of error have reliably had asymmetrical cost EMT also predicts the direc tion of bias which will be toward making the less costly of the two errors Some of the effects we have reviewed were predicted in advance using error man agement logic These include commitment underperception by women Haselton amp Buss 2000 overinclusiveness of disease avoidance e g Faulkner et al in press Park et al 2003 the use of the social exchange heuristic Yamagishi et al 2003 and neg ative forgiveness bias Friesen et al 2005 Just as many such situations have already been studied there may be many more that have not yet been the subject of empirical investigations We have already described several new predictions We suggested that the personality domains in which the FAE is particularly likely to occur will be those that are most likely to impose fitness costs such as aggres siveness and deceitfulness In the previous section we proposed that the cultural differences in the domains in which positive illusions occur will be linked to cultural differences in the value of those domains Qualities or outcomes that are universally valued such as the pres ervation of health will vary little across cultures EMT also predicts that discrepancies between judgments about outcomes the participant controls will often show different biases to those not in the participant s control as in the result that people believe their own life to be getting better but life in general to be getting worse Such effects might be elicited in many different domains For example in a simulation of the transmis sion of a disease EMT predicm that people should be overly fearful that others are infectious but overly op timistic that their own attempts to avoid contagion will be effective We also suggested that pregnant women will express diseaseavoidance attitudes that are espe cially strong or overinclusive Haselton amp Buss 2000 predicted two biases in the domain of sexuality and courtship We suggest two more The first is a bias in inferring the romantic or sexual interest of others in one s mate and the second a bias in inferring the interest of one s mate in others First the fitness costs of failing to recognize the inter est of an interloper in one s mate and to lose one s mate as a result are high One must reinitiate mate search pay new costs associated with courtship and attraction and risk the loss of investment from the mate in exist ing offspring The costs of somewhat elevated vigi lance especially if activated only in situations present ing plausible threat would be comparatively low Thus we predict the interloper effect a bias toward overinferring the sexual interest of others in one s mate in ambiguous or mildly threatening situations For ex ample at a cocktail party if an attractive other behaves in a friendly and animated fashion toward ego s mate ego will assume greater sexual interest on the part of the other than will an independent onlooker This bias would function we propose to increase materetention efforts and help to ward off defection Smurda and Haselton 2002 documented evidence suggestive of the interloper bias They found that people involved in committed relationships tended to rate the sexual inter est of samesex others eg based on a smile more highly than people not involved in relationships Maner and colleagues Maner et al 2003 found that women in committed relationships showed a greater 61 HASELTON AND NETI39LE attentional and memorial bias for attractive female faces than women not in relationships providing addi tional suggestive evidence of the interloper bias Second the fitness cosm to a man of failing to detect partner infidelity are high His own reproduction can be delayed for the course of a pregnancy at minimum He also risks investing time and resources in the off spring of a reproductive competitor However the cosm of false alarms are also plausibly high Undue suspi cion can damage relationships and time spent on un needed monitoring of the partner results in missed op portunities to pursue other fitnessenhancing activities such as the collection of food or providing care for kin Thus there is a delicate balance between the costs of errors in infidelity detection also see Buss 2000 This balance shifts however over the course of the woman s menstrual cycle As ovulation nears fertility increases and the risks to a man of cuckoldry are at their highest Therefore we propose a bias in men to ward overinferring extrapair sexual interest and in extreme cases infidelity when a his partner is near ing midcycle and b he is confronted with ambiguous cues to infidelity such as his partner s expressed friendliness to another man This general logic also predicm that the interloper bias discussed previously may become acute for men when their partners are most fertile These predictions are rendered plausible by recent evidence suggesting that men have adapta tions sensitive to their partner s fertility status For ex ample women s body scent including scent samples taken from the torso and upper body and samples of vaginal secretions is rated as most attractive during the high fertility phase of the cycle Doty Ford Preti amp Huggins 1975 Singh amp Bronstad 2001 Thornhill et al 2003 Women also report increased love attrac tion sexual proprietariness and jealousy expressed by their partners near ovulation as compared with other cycle phases Gangestad Thornhill amp Garver 2002 Haselton amp Gangestad 20051 One of the best researched examples we have dis cussed is the easily elicited fear of snakes and spiders Snakes and spiders were not the only dangerous ani mals in ancestral environments Predatory cats and 1Note however that these studies do not demonstmte bias in men s inferences of women s proclivity toward in delity There are at least three possible explanations for this effect a given that mens our lmtdat 394 1 4o other large mammals as well as large reptiles such as crocodiles have likely played a role in the evolutionary history of humans and have shaped a predator avoid ance psychology in humans B arrett 1999 Therefore we predict that the same effects documented for snakes and spiders will be documented for these other ances trally dangerous animals Moreover we hypothesize that the environmental cues that reliably increased sus ceptibility to injury should increase false alarm rates in the detection of these animals and in inferences of their dangerousness One such cue is ambient darkness S challer et al 2003 Darkness and states of fear should also amplify other protective biases including auditory looming estimating early arrival of ap proaching objects Bias Versus Accuracy Krueger and Funder 2004 raised questions about the obsessional focus of many psychologists on bias and error which has led to an unnecessarily dreary outlook on human cognition and a failure to study how accurate judgments are actually made In the studies we have reviewed our focus on documented biases does not imply that people are usually or of ten wildly off base In the Haselton and Buss studies 2000 men and women showed remarkable agree ment about how much commitment or sexual interest each dating cue communicated with correlations above 90 But at the same time men overestimated women s sexual interest and women underestimated men s commitment Likewise in the forgiveness bias studies partners tended to agree on whether one part ner had forgiven the other with a maximum correla tion of 44 but they still tended to underestimate how much they had been forgiven Friesen et al 2005 Thus as Fletcher 2002 noted bias and accu racy can vary quite independently and systematic bias does not preclude a tether to reality The criteria for predicting bias are different from those for predicting accuracy An error management bias is predicted when errors differ reliably in their costs Accuracy or judgmental sensitivity is predicted when valid cues are available Funder 1995 and the fitness consequences of correct discrimination are largeifor example in judging the dominance or r al 2002 Haselton amp Gangestad 2005 men could be tracking acr tual risk through their partner s behavior and adjusting their mate guarding accordingly b women s perceptions of their partners ber L u A or just their materguarding efforts when their partners are most fertile and hence they are at greatest risk of cuckoldry The hypothesis we advance is a version of c that men use ovulatory cues to adjust mate guarding and that they become biased toward false alarms in their inferences of their partner s extmrpair sexual interest and be havior Controlled laboratory experiments may be required to test the infidelityrbias hypothesis 62 orientation of others Gangestad Simpson DiGeronimo amp Biek 1992 If the fitness consequences of discrimination are large and there is a differential cost of errors in one direction or the other then a judgmental system should be both sensitive and biased In courtship it is important to recognize that some cues are greater indicators of sexual interest than others smiling vs stroking one s date on the thigh but it also pays to overestimate the degree to which cues indicate interest if it helps a man to avoid a miss PARANOID OWMISTOGNIHW BIASES The Rational Actor An important reason for seeking an explanatory framework for biases concerns the adequacy of human reasoning Much social theory particularly in econom ics and political science depends on conceptualizing the individual as a rational actor able to use informa tion available to him or her in an optimal way given his or her aims and objectives If people turn out not to be rational in the required sense such models lack valid ity Experimentally and observationally based re search such as that carried out by social psychologists anthropologists and experimental economists has of ten cast doubt on the accuracy of the rational actor as sumption Bell 1995 Davis amp Holt 1993 Kahneman et al 1982 However if observed departures from ra tionality are studied piecemeal and accepted as merely quirks of human beings without seeking deeper expla nation social science becomes balkanized between theorists who have a powerful explanatory framework that lacks validity and empiricists who have an accu rate list of phenomena but no explanations HermannPillath 1994 Nettle 1997 Moreover the outlook for human rationality becomes bleak because the implication is simply that people because of limi tations in cognitive machinery are not capable of opti ma1 decision makin The reinterpretation of many biases as design fea tures rather than design defects suggests a different perspective Both the content and direction of biases can be predicted theoretically and explained by optimality when viewed through the long lens of evo lutionary theory Thus the human mind shows good design although it is design for fitness maximization not truth preservation This reorientation accords with other recent work in psychology For example the heuristics and biases tradition Kahneman et al 1982 saw the mind as made up of simple problemsolving tools that although functional over a restricted rang of 39 are imply 39 q pr 4quot p timal judgment in general resulting in a wide range of cognitive illusions or pervasive departures from optimality More recent work however has questioned this bleak view Some cognitive illusions disappear or greatly attenuate when the task is presented in an eco logically valid format Cosmides amp Tooby 1996 Gigerenzer amp Hoffrage 1995 Ecological validity a longstanding but undertheorized term in psychology may in effect be equated to the task format approximat ing some task that humans have performed recurrently over evolutionary time Moreover many of the simple heuristics that people actually use perform just as well as complex normative models under realworld conditions of partial knowl edge Gigerenzer amp Todd 1999 There are even cir cumstances in which they perform better than norma tive modelsithe socalled lessismore effect The lessismore effect occurs because simple heuristics can exploit structural features of the decisionmaking environments that are noisy and uncertain and contain multiple cues EMT complements the lessismore principle with a biased is better principle under some circumstances which can be predicted in a prin cipled way biased strategies are actually superior to nonbiased ones Conclusion EMT predicts that over a certain set of conditions biased reasoning strategies can be adaptive Most im portant where error costs are known and asymmetric and there is uncertainty about events a biased reason ing strategy can actually do better than an unbiased one It strikes us that these conditions are likely to char acterize many of the real dilemmas that have faced us and our ancestors Because dilemmas are never re peated with exactly the same parameters events are hard to predict accurately However the payoffs for various kinds of outcomes from being bitten by a snake to obtaining a mate are recurrently positive or negative over evolutionary time Thus EMT predicts that highly specific biases should evolve EMT is an additional element in a picture of the mind as a welldesigned instrument for solving the kinds of problems that have faced human beings over their evolutionary history Many apparent quirks of hu man thought from our fear of harmless spiders to our superstition and paranoia to our eternal optimism may be optimal adaptations to the worlds in which we have lived References Abbey A 1982 Sex differences in attributions for friendly behave ior D males misperceive females friendliness Journal of Personality and Social Psychology 42 83838 Abbey A amp Harnish R J 1995 Perception of sexual intent The role of gender alcohol consumption and mpe supportive attir tudes Sex Roles 32 977313 Abbey A amp Melby C 1986 The effects of nonverbal cues on gender differences in perceptions of sexual intent Sex Roles 15 2837298 Abmmson L Y Seligman M E P amp Teasdale J D 1978 Learned helplessness in humans Critique and reformulation Journal ofAbnormal Psychology 87 49774 Alloy L B amp Abmmson L Y 1979 Judgment of contingency in depressed and nonrdepressed subjects Sadder but wiser Jour nal of Experimental Psychology General 108 4437479 Andrews P W 2001 The psychology of social chess and the evor lution of attribution mechanisms Explaining the fundamental attribution error Evolution and Human Behavior 22 11729 Atmn S 2002 In gods we trust The evolved landscape ofreligion New York Oxford University Press 63 HASELTON AND NETI39LE Atmn S amp Norenzayan A 2005 Religion s evolutionary land scape Counterintuition commitment compassion commur nion Behavioral and Brain Sciences 87 7137770 Barrett H C 1999 Human cognitive adaptations topredators and prey Unpublished doctoral dissertation University of Califorr nia Santa Barbam Barrett H C Todd PM Miller G F amp Blythe P W 2005 Acr umte judgments of intention from motion cues alone A crossrcultural study Evolution and Human Behavior 26 3137331 Baumeister R F ampLeary M R 1995 The need to belong Desire or interpersonal attachments as a fundamental human motivar tion Psychological Bulletin 117 4977529 Bell D 1995 On the nature of sharing Beyond the range of methr odological individualism CurrentAnthropology 36 8267830 Bishop G D Alva A L Cantu L ampRittiman R K 1991 Re sponses to persons with AIDS Fear of contagion or stigma Journal o Applied Social Psychology 21 187771888 Bloom P amp Veres C 1999 The perceived intentionality of groups Cognition 71 B17B9 Bouskila A amp B1umstein D T 1992 Rules of thumb for predar tion hazard assessment Predictions from a ynamic model American Naturalist 139 1617176 Bowles S amp Gintis H 2002 Homo reciprocans Nature 415 1257128 Brewer M B 1979 Ingroup bias in the minimal intergroup situar mm 86 30 7 24 Brown J D 1986 Evaluations of self and others Selfrenhancer ment biases in socialjudgments Social Cognition 4 3537376 Buss D M 1994 The evolution ofdesire Strategies ofhuman mating New York Basic Books Buss D M 2000 The dangerouspassion Whyjealousy is as nec essary as love and sex New York Free Press Camerer C amp Thaler R 1995 Ultimatums dictators and many ners Journal ofEconomic Perspectives 9 7356 Campbell J D 1986 Similarity and uniqueness The effects of at tribute type relevance and individual differences in selfresteem and depression Journal ofPersonality and Social Psycholog 50 2817294 Caporael L Dawes R M Orbell J M amp van der ngt A J 1989 Sel shness examined Behavioral and Brain Sciences 12 6837739 Cashdan E 1998 Adaptiveness of food learning and food averr sions in children Social Science Information 37 6137632 Catania A C amp Cutts D 1963 Experimental control of superstir tious responding in humans Journal ofthe ExperimentalAnal ysis ofBehavior 6 2037208 Choi I Nisbett R E amp Norenzayan A 1999 Causal attribution across cultures Variation and universality Psychological Bul letin 6 Cosmides L 1989 The logic of social exchange Has natuml ser lection shaped how humans reason Cognition 31 1877276 Cosmides L amp Tooby J 1996 Are humansgood intuitive statistir cians after all Rethinking some conclusions from the literature onjudgment under uncertainty Cognition 58 17 3 Cosmides L amp Tooby J 2000 Evolutionary psychology and the emotions In M Lewis amp J M Havilanerones Eds Handbook of emotions 2nd ed pp 917115 New York Guilford Crocker J ampPark L E 2003 Seeking selfresteem Construction maintenance and protection of selfrworth In M R Le amp J P Tangney Eds Handbook ofselfand Mentity pp 2917313 New York Guilford Daly M amp Wilson M I 1988 Homicide Hawthorne NY de Gruyter Davis D D amp Holt C A 1993 Experimental economics Princer ton NJ Princeton University Press 64 de Jong P amp Merckelbach H 1991 Covariation bias and electroden39nal quot 39 quot r quot L c J c L havioural treatment Behaviour Research and Therapy 29 30 7314 Doty R L Ford M Preti G amp Huggins G R 1975 Changes in the intensity and pleasantness of human vaginal odors during menstrual cycle Science 190 131671317 aller M Park J A amp Duncan L A 2004 volved disease avoidance mechanisms and contemporary xer nophobic attitudes Group Processes and Intergroup Relations Faulkner J Sch E 7 33 7 Fenigstein A 1984 Selfrconsciousness and the overperception of self as a target Journal ofPersonality and Social Psychology 47 86870 Fessler D M T 2002 Reproductive immunosuppression and dietiAn evolutionary perspective on pregnancy sickness and meat consumption CurrentAnthropology 43 1 761 Fletcher G 2002 The new science of intimate relationships Oxr ford England Blackwell Fox E Russo R amp Dutton K 2002 Attentional bias for threat Evidence for delayed disengagement from emotional faces Cognition and Emotion 16 3557379 Friesen M D Fletcher G J O amp OverallN C 2005 A dyadic assessment of forgiveness in intimate relationships Personal Relationships 12 61777 Funder D C 1995 On the accumcy of personalityjudgment Arer alistic approach Psychological Review 102 6527670 Gangestad S W Simpson J A DiGeronimo K amp Biek M 992 Differential accuracy in person perception across tmits Examination of a functional hypothesis Journal ofPersonality and Social Psychology 62 6887698 Gangestad S W Thornhill R amp Garver C E 2002 Changes in women s sexual interests and their partners mate retention tacr tics across the menstrual cycle Evidence for shifting con icts of interest Proceedings ofthe Royal Society ofLondon B Bio logical Sciences 269 9757982 Garcia J Ervin F R amp Koelling R A 1966 Learning with pro longed delay of reinforcement Psychonomic Science 5 12 22 Gigerenzer G amp Hoffrage U 1995 How to improve Bayesian reasoning without instruction Frequency formats Psychologi cal Review 102 6847704 Gigerenzer G amp Todd P M 1999 Simple heuristics thatmake us smart Oxford England Oxford University Press Green D M amp Swets J A 1966 Signal detection and psychophysics New York Wiley Greenberg J Pyszczynski T Solomon S amp Pinel E 1993 Eff fects of selfresteem on vulnerabilityrdenying defensive distorr tions Further evidence of an anxietyrbuffering function of selfresteem Journal of Experimental Social Psychology 29 22 7251 Guthrie S 2001 Why Gods A cognitive theory In J Andresen Fdxnr39 39 39 F quot 39 riinl lief ritual and experience pp 947112 Cambridge England ambridge University Press Hagerty M R 2003 Was life better in the good old days 1 1 u u 1 1 n v ness Studies 4 1157139 Haselton M G 2003 The sexual overperception bias Evie dence of a systematic bias in men survey of naturally occurring events Journal ofResearch in Personality 371 4347 Haselton M G amp Buss D M 2000 Error management theory A E r r I LI I I 39 quot 1m Inf Personality and Social Psychology 78 81791 Haselton M G amp Gangestad S W 2005 Conditional exp PARANOlD OPI llVIIST7COGNITIVE BIASES Heider F Simmel S 1944 An experimental study of apparent behavior American Journal ofPsyc o ogy 57 4 7 59 Heine S J Lehman D R Markus H amp Kitayama S 1 there a universal need for positive self7regard Psychological Review 106 7667794 Henrich J amp Boyd R 2001 Why people punish defectors Con7 f rmist tmnsmission stabilizes cos y enforcement of norms in coopemtive dilemmas Journal of Theoretical Biology 208 79789 Henrich J Boyd R Bowles S Camerer C Gintis H McElreath R et al 2001 In search ofHomo economicus Experiments in 15small7scale societiesAmericanEconomicReviem 9 737 9 Hermann7Pillath C 1994 Ecological mtion ty Homo economicus and the origins of the social order Journal ofS cial and Evolutionary Systems 17 7 Hurtado A M amp Hill K R 1992 Paternal effect on offspring survivorship among Ache and Hiwi hunter7gatherers In B S Hewlett et al Eds Fatherchild relations Cultural and biosocial contexts pp 31755 New o ruyt r Johnson C B Stockdale M S amp Saal F E 1991 Persistence of m misperceptions of friendly cues across a variety o inter7 personal encounters Psychology of Women Quarterly 15 463717 Johnson D 2004 Overcon dence and war The havoc and glory of positive illusions Cambridge MA Harvard University Press Kahneman D Slovic P amp Tversky A Eds 1982 Judgement nder uncertainty Heuristics and biases Cambridge England Cambridge University Press Keeley L H 1996 War before civilization The myth ofthe peace ful savage New York Oxford University Press Kitayama S Markus H ats m to Norasakkunkit V 1997 Individual and collective processes in the construction of the self Self7enhancement in the United States and self7criti7 cism in Japan Journal ofPersonality and Social Psychology 72 124571267 Kmmer R M 1994 The sinister attribution error Pamnoid cogni7 tion and collective distrust in organizations Motivation and Emotion 18 1997230 Kmmer R M 1998 Paranoid cognition in social systems Thinking and acting in the shadow of doubt Personality and Social Psychology Review 2 2517275 Krebs D L amp Denton K 1997 Social illusions and self7decep7 tion The evolution of biases in person perception In J A Simpson amp D T Kenrick Eds Evolutionary socialpsychol ogy pp 21747 Hillsdale NJ Lawrence Erlbaum Associates Krueger J I amp Funder D C 2004 Towards a balanced social psychology Causes consequences and cures for the prob7 lem7seeking a roach to social behavior and cognition Behav ioral and Brain Sciences 27 3137376 Kunda Z 1990 The case for motivated reasoning Psychological Bulletin 108 480 498 Kurzban R amp Leary M R 2001 Evolutionary origins of stigma7 tization The functions of social exclusion Psychological Bul letin 123 1877208 Kurzban R Tooby J amp Cosmides L 2001 Can mce be erased Coalitional computation and social categorization Proceedings ofthe NationalAcademy ofSciences 98 15387715392 Langer E J 1975 The 39 usion of control Journal ofPersonality and Social Psychology 32 3117328 Langer E J amp Roth J 1975 Heads I win tails it s chance The il7 1usion of control as afunction of the sequence of outcomes in a purely chance task Journal ofPersonality and Social Psychol ogy 32 9517955 Lima S L amp Dill L M 1990 Behaviouml decisions made under e risk of predation Areview and prospectus Canadian Jour nal onoology 68 6197640 Maner J K Kenrick D T Becker D V De1ton A W Hofer B amp Wilbur C J et al 2003 Sexually selective cognition Beauty captures the mind of the beholder Journal ofPersonal ity and Social Psychology 85 110771120 Maner J K Kenrick D T Becker V Robertson TE Hofer B Neuberg S L et al 2005 Functional projection How funda7 mental social motives can bias interpersonal perception Jour nal ofPersonality and Social Psychology 88 63778 Matute H 1994 Learned helplessness and superstitious behavior as opposite effects of uncontrollable reinforcement Learning and Motivation 25 2167232 Matute H 1995 Human reactions to unavoidable outcomes Fur7 ther evidence for superstitions mther than helplessness Quar terly Journal ofExperimental Psychology 48 1427157 McKenna F P 1993 It won t happen to me Unrealistic optimism or illusion of control British Journal of Psychology 841 3 7 0 Miller D T amp Ross M 1975 Self7serving biases in the attribu7 tion of causality Fact or fiction Psychological Bulletin 82 2137225 Mineka S 1992 Evolutionary memories emotional processing and the emotional disorders Psychology ofLearning andMoti vation 28 1617206 Nesse R M 2001 The smoke detector principle Natuml selection a d the regulation of defensesAnnals ofthe New YorkAcademy ofSciences 935 75785 Nesse R M 2005 Natuml selection and the regulation of de7 fenses A signal detection analysis of the smoke detector prob7 lem Evolution and Human Behavior 26 887105 Nettle D 1997 On the status of methodological individualism CurrentAnthropology 38 837286 Nettle D 2004 Adaptive illusions Optimism control and human mtionality In D Evans amp P Cruse Eds Emotion evolution and rationality pp 1937208 Oxford England Oxford Uni7 versity Press Neuhoff J G 1998 Perceptual bias for rising tones Nature 395 Neuhoff J G 2001 An adaptive bias in the perception of looming auditory motion Ecological Psychology 132 877110 Nisbett R E Cabuto C Legant P amp Marecek J 1973 Behav7 ior as seen by the actor and as seen by the observer Journal of sonality and Social Psychology 27 1547164 Norenzayan A Choi I ampNisbett R E 2002 Cultuml similari7 ties and differences in social inference Evidence from behav7 ioral predictions and lay theories of behavior Personality and Social Psychology Bulletin 28 1097120 Ohman A amp Soares J J 1993 On the automatic nature of phobic fear Conditioned electrodermal responses to masked fear7rele7 vant stimuli Journal ofAbnormal Psychology 102 1217132 Ono K 1987 Superstitious behaviorin humans Journal ofthe Ex perimental Analysis ofBehavior 47 2 7271 Park J H Faulkner J amp Schaller M 2003 Evolved dis7 ease7avoidance processes and contemporary anti7social e av7 ior Prejudicial attitudes and avoidance of people with disabili7 ties Journal ofNonverbal Behavior 27 65787 Park J H Schaller M amp Cmndall C S 2004 Obesity as a heu ristic cue connoting contagion Perceived vulnerability to dis ease promotes anti fat attitudes Unpublished manuscript Uni7 versity of British Columbia Canada Pmtto F P amp John O P 1991 Automatic vigilance The atten7 tion7grabbing power of negative social information Journal of Personality and Social Psychology 61 38391 Price M Cosmides L ampTooby J 2002 Punitive sentiment as an anti7free rider psychological adaptation Evolution and Human Behavior 23 2037231 Quillian L amp Pager D 2001 Black neighbors highercrime The roleofmcial 39 quot f 39 LL L J 39 American Journal ofSociology 107 7177767 65 GreedoidBased Noncompensatory Inference Michael Yee Ely Dahan John R Hauser James Orlin June 27 2005 Under review at Marketing Science 2quotd round Michael Yee is a graduate student at the Operations Research Center E40149 Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge MA 02139 617 2536185 myeemitedu Ely Dahan is an Assistant Professor of Marketing at the Anderson School University of Califor nia at Los Angeles 110 Westwood Plaza B514 Los Angeles CA 90095 310 2064170 fax 310 2067422 edahanuclaedu John R Hauser is the Kirin Professor of Marketing Sloan School of Management Massachu setts Institute of Technology E56314 38 Memorial Drive Cambridge MA 02142 617 253 2929 fax 617 2537597jhausermitedu James Orlin is the Edward Pennell Brooks Professor of Operations Research and Codirector MIT Operations Research Center Massachusetts Institute of Technology E40147 77 Massachusetts Avenue Cambridge MA 02139 617 2536606jorlinmitedu This research was supported by the MIT Sloan School of Management the Center for Innovation in Product Devel opment at MIT the Operations Research Center at MIT and by the Office of naval Research contract N0001498 10317 This paper may be downloaded from httpmitsloanmiteduvc Our special thanks to Peter Lenk who kindly and unselfisth shared data with us We wish to thank Ashvini Thamm aiah who assisted in the development and pretesting of the webbased questionnaire The study benefited from comments by numerous pretests at the MIT Operations Research Center and the Kappa Alpha Theta Sorority at MIT Sm artPhone images produced by R Blank Our thanks to Theodoros Evgeniou Shane Frederick Steven Gaskin Rej eev Kohli and Olivier Toubia for insightful comments on an earlier draft This paper has benefited from presentations at the MIT Operations Research Center the Center for Product Development the MIT Marketing Group Seminar Mchigan s Ross School of Business Seminar Series the 2004 Marketing Science Conference in Rotterdam The Netherlands the 2005 Marketing Sci ence Conference at Emory University the AMA s 2004 Advanced Research Techniques Forum Whistler BC the 2004 Explor Award Case Study Showcase in New Orleans LA the 2004 Management Roundtable Voiceofthe Customer Conference Boston MA and the Marketing Camp at Columbia University The final three names are listed alphabetically Contributions were extensive and synergistic GreedoidBased Noncompensatory Inference Abstract We propose practical methods to estimate the best noncompensatory description of re spondents decision processes Estimation is a nontrivial combinatorial problem which has hitherto been computationally infeasible for practical problems Greedoid languages provide a structure and theory to transform this problem and decrease estimation time by a factor of ap proximately 1013 for practical l6aspect problems The methods work with fullrank partial rank considerthenrank consideronly or choice data and are readily extended to situations where the researcher believes that some rank judgments are more accurate than others We compare the predictive ability of Greedoid methods to two additive models LIN MAP and hierarchical Bayes ranked logit HBRL Greedoid methods predict comparatively well doing significantly better on both holdout pairs and hit rates for SmartPhones 339 respon dents For computers data from Lenk et al 1996 Greedoid methods do as well as HBRL on hit rates and almost as well as HBRL on holdout pairs Greedoid methods applied to consider thenrank data are particularly attractive because predictive ability is quite good and the respon dent s task takes less time increases completion rates and is perceived as more enjoyable more accurate and more interesting The data suggest that most respondents 65 for SmartPhones 58 for computers use a lexicographic processing rather than a qcompensatory model We find that sorting and the number of profiles does not increase lexicographic processing but the nature of the task full rank vs considertherank does increase lexicographic processing We find further that most re spondents process profiles by aspects rather than features We close with managerial implications We expect Greedoid methods to be particularly attractive for product categories in which respondents are asked to evaluate a large number of potential choices such as automobiles or consumer electronics Keywords Lexicography Noncompensatory decision rules Choice heuristics Optimization methods in marketing Conjoint analysis Product development GreedoidBased Noncompensatory Inference 1 NonCompensatory Decision Processes Personal digital assistants PDAs are popular productivity enhancing tools Our univer sity s approved supplier GovConnection offers 97 PDAs from which we can choose Local re tailers also have moderately broad product lines 21 at Circuit City 25 at Staples 27 at Micro center and 33 at CompUSA Websites often provide tools to simplify PDA choice for consum ers For example Staples CompUSA Circuit City and Micro Center encourage consumers to selforganize choice sets by operating system brand price or other features Figure 1 This re tail environment is consistent with but not proof of a decision process in which consumers evaluate products by a heuristic process Consumers might first choose an operating system then a price range and then a brand Only then might they make choose a PDA by allowing some features to compensate for the lack of a desired feature Figure 1 PDAs Available from Micro Center CompUSA Staples and Circuit City the center nFanuter shnpning mmsmppmgaag Cum Support I I In r w gt Category See h 1 online Pas isquot roducm hit Category Search 3919 Producm in this category include I IOW E5 prices mm 31 CumguiersKPDA s V gm PDAs 8 Handheld PCs m s PDAsr Palm Puwered s PDAsr PuckeiPC Based p ram 1a rim There is ample evidence in the psychology consumerbehavior and marketingscience literatures that consumers simplify consideration andor choice with a heuristic process eg Bettman Luce and Payne 199839 Broder 200039 Einhom 1970 Gigerenzer and Goldstein 199639 Martignon and Hoffrage 2002 Heuristic simplification is more likely when the initial set of products is large eg Johnson and Meyer 198439 Payne Bettman and Johnson 1993 Many re searchers suggest further that the heuristics might best be described at least paramorphically by a considerthenchoice decision process eg Bettman and Park 198039 Einhom and Hogath GreedoidBased Noncompensatory Inference 1981 Gensch 1987 Hauser and Wemerfelt 1990 Montgomery and Svenson 1976 Payne 1976 Payne Bettman and Johnson 1993 Roberts and Lattin 1991 Heuristic decision processes are important and interesting scienti cally and managerially Firstly researchers in consumer behavior are interested in studying when if heuristic processes are used By using a variety of methodologies ranging from verbal process tracing to informa tion display mechanisms e g Mouselab researchers have studied how consumers adapt and or construct decision processes based on the characteristics of the decision environment see Payne Bettman and Johnson 1993 for a review Some researchers suggest that heuristic processes might even be appropriately robust strategies for consumers and that such strategies are based in evolution Chase Hertwig and Gigerenzer 1998 Dawes 1979 Dawkins 1998 From a policy perspective the popularity of webbased virtual advisors suggests that consumers nd value in heuristics that help them search categories that contain many brandfeature combinations Secondly the identification of heuristic processes is important managerially Not only does it inform retailers and website designers how to organize their shelves and websites but it suggests to product designers which features to include and to advertisers how they might pre sent products and choices to consumers For example in the automobile market consumers consider fewer than 5 of the makemodel combinations available 510 out of 350 Urban and Hauser 2004 In consumer packaged goods knowing the consideration set can explain up to 80 ofthe uncertainty in choice Hauser 1978 A big part ofthe battle for sales is won ifa manufacturer can design products that survive the rst stages of a decision heuristic so that they are at least considered In advertising knowledge of consumers heuristics might suggest which features to stress in positioning or in unique selling propositions e g Batra Myers and Aaker 1996 Ogilvy 1985 Reeves 1961 In this paper we explore new methods to study heuristic decision processes These meth ods use Greedoid languages and dynamic programming to solve combinatorial computational problems signi cantly more ef ciently than as reported in the extant literature We demonstrate how the methods can be used to identify the heuristic decision processes that best describe ob served consideration and or choice Because the methods work with either rankorder data or considerthenrank data we are able to examine empirically which datacollection format best predicts choice A considerthenrank task may be more enjoyable and less effortful for respon dents eg Malhotra 1986 Oppewal Louviere and Timmermans 1994 Srinivasan and Park GreedoidBased Noncompensatory Inference 1997 and hence might mean shorter questionnaires less cost and may encourage more re spondents to complete the task fewer nonresponse issues The paper proceeds as follows In the next section we brie y review the literature on heuristic processes and provide examples A subsequent section describes the respondents tasks We then present Greedoidbased methods to estimate noncompensatory heuristics and discuss the traditional methods to which they are compared We then test the methods and the twostage respondent task empirically in a 2X2 experiment in which 339 respondents choose from a 32 SmartPhones chosen from a fractional factorial 4324 design We examine the impact of the number of pro les the respondents task and sorting on the tendency of respondents to use noncompensatory processes For comparison we reanalyze classic data in which 201 re spondents rated 16 computers chosen from a fractional factorial 213 design The data illustrate the contingency of heuristic processing 7 we chose SmartPhones because we expected that heuristic processes are better able to describe how respondents evaluate SmartPhones In contrast a pri ori we expect the features of computers to be more compensatory We close by illustrating how Greedoid analysis provides managerial insight 2 Brief Review of Potentially Noncompensatory Decision Processes We consider decision processes in which products are represented by their features and consumers must decide which product to purchase or consume While the process by which con sumers encode products into features can be complex and important Einhom and Hogarth 1981 this topic is beyond the scope of this paper Our scope includes situations in which such encoding is feasible and reasonably descriptive of consumer decision processes For practical applications we might use voiceofthecustomer methods to identify a representative set of fea tures eg Griffin and Hauser 1993 Zaltman 1997 When a feature is binary it is called an as pect eg Tversky 1972 Multilevel features can be considered collections of aspects that are related Verizon vs Cingular vs Nextel vs Sprint for SmartPhone service providers A profile is the feature or aspect description of a product Noncompensatory Processes In a compensatory process high levels on some aspects can compensate for low levels on other aspects In a noncompensatory process high levels on some aspects may not compensate for low levels on other aspects One wellknown noncompensatory process is a lexicographic process consumers evaluate profiles first by one feature then another until a judgment or choice GreedoidBased Noncompensatory Inference is made Fishbum 1974 Nakamura 2002 For example consider an illustrative example in which consumers rank playing cards that differ on the features of suit and value As illustrated by the first row of Figure 2 a consumer might rank first on the feature of suit putting all spades first then hearts then diamonds and lastly clubs and then rank on the feature of value within suit by putting all Aces before Jacks We call this process lexicographic by features LBF Figure 2 Examples of Lexicographic Heuristic Processes quotraigiy m Diverge Simplifying as Ranking First by 2nd 3rd by4th 5th 6th 7th Last Heuristic Acronym Rule Choice Choice Choice Choice Choice Choice Choice Choice 7 gt 7 gt 7 gt 7 L h 3233 LBF A gt J A J Acceptance ABA A 7 7 By Aspects g D 42553 EBA 399 El Lexicographic By LBA 7 A 7 Other heuristics are possible A consumer might rank playing cards by M say ac cepting rst spades then Aces then hearts and finally diamonds until all playing cards are ranked second row of Figure 2 Whenever there is a tie the consumer moves to the next as pect in the lexicographic order For ease of reference we call such processes acceptance by as pects ABA ABA is related to Tversky s eliminationbyaspects process EBA in which con sumers successively eliminate aspects as shown in the third row of Figure 2 Tversky defines EBA as a random process in which the probability that an aspect is chosen is proportional to its measure In this paper we follow Johnson Meyer and Ghose 1989 Montgomery and Svenson 1976 Payne Bettman and Johnson 1988 and Thorngate 1980 and use EBA to refer to a deterministic process in which an aspect order is given Finally consumers may mix acceptance and elimination criteria We call such a mixed process lexicographic by aspects LBA Be cause ABA and EBA are special cases of LBA we focus on LBA When a feature has more than two aspects eliminating an aspect clubs is the same as accepting its complement spades U hearts U diamonds but EBA is not equivalent to an ABA GreedoidBased Noncompensatory Inference process of accept spades then hearts then diamonds The ABA process orders spadeshearts diamonds while the EBA process does not However for twolevel aspects there exists an equivalent EBA process for every ABA process Figure 3 illustrates this equivalency for playing cards that differ on three binary aspects suit value and shape Figure 3 Equivalent Processes for Binary Features Two Aspect Features TLA F 2 d Mm 395 quot Slmphfy39 L y My Choice Choice Choice Choice Choice Choice Choice Choice u Heuristic lm LBF gt armor by Features 7 gt 4 A ha 522 ABA 2D 7 EBA by Aspects LBA D 7 ABA EBA LBA and LBF de ne orderings and hence can be used to explain either full or partial rankings including respondent tasks such as rank all pro les choose a single pro le or indicate which pro les are worth further consideration Finally the processes can be modi ed to include constraints within features such as lower prices are always preferred to higher prices Compensatory Processes Many authors represent a compensatory process as an arithmetic rule in which each as pect receives a weight and consumers sum the weights associated with the aspects in a pro le to form utility Consumers then choose the product with the highest utility However not all sets of aspect partworths imply a compensatory process Ifthe aspect partworths follow an ap propriate geometric sequence eg 2139quot for the n3911 aspect then an additive model produces a lexicographic process in which no set of lower ranked aspects can compensate for the lack of a higher rank aspect Jedidi Kohli and DeSarbo 1996 Kohli and Jedidi 2004 Olshavsky and Acito 1980 Thus we will reserve the word compensatory for additive models that are truly compensatory eg when the partworths are constrained so that they are not too extreme GreedoidBased Noncompensatory Inference Constructive Processes Research suggests that consumer decision processes are contingent on many context ef fects including the range of aspects correlation among aspects baserate information reference points the size of the choice set the relevance of the decision and the difficulty of comparison see review in Payne Bettman and Johnson 1993 For example we expect most respondents to use a noncompensatory process when the number of products is large as in our PDA example or our empirical test with 32 SmartPhones pro les eg Johnson and Meyer 1984 We expect the more respondents to use a compensatory process with fewer profiles 7 say 16 computers Many 39 n quot explain 1 n r y processes Some hypotheses rely on a cost bene t tradeoff between effort and decision accuracy e g Shugan 1980 Other hypotheses suggest that noncompensatory processes are inherently more robust and are best suited for judgment tasks when preferences are to be constructed when consumers are uncertain about the valuations of the aspects or when emotion and rationality are integrated eg Luce Payne and Bettman 1999 Martignon and Hoffrage 2002 From our perspective we seek to identify the process that best explains the observed data holdouts To the extent that data collection ap proximates the essential characteristics of real choice environments the methods provide insight about the processes that are used in these environments Existing Methods to Infer Noncompensatory Processes Because decision processes might be contingent measurement of consumer decision processes attempts to approximate the conditions under which real consumers make decisions Many measurement examples in the marketing science literature are consistent with non compensatory decision processes For example both Srinivasan and Wyner s 1988 Casemap and Johnson s 1991 Adaptive Conjoint Analysis ACA include steps in which respondents are asked to eliminate unacceptable levels Because this task is often difficult for respondents Green Krieger and Bansal 1988 Klein 1988 other researchers have attempted to infer the elimination process in a single estimation step DeSarbo et a1 1996 Gilbride and Allenby 2004 Gensch 1987 Gensch and Soof1 1995 Jedidi and Kohli 2004 Jedidi Kohli and DeSarbo 1996 Kim 2004 Roberts and Lattin 1991 Swait 2001 For example Gilbride and Allenby 2004 p 399 use hierarchical Bayes methods to analyze choicebased conjoint data to infer screening rules for cameras They estimate that 58 of the respondents screen on a single fea ture 33 on two features 2 on three features and 8 use fully compensatory processes GreedoidBased Noncompensatory Inference In psychology Broder 2000 analyzes choices among two pro les described by four as pects He compares the t of an unconstrained additive model to two additive models 1 a model with the aspects 39 J to 21 n n r y and 2 an additive model with equal weights Dawes 1979 model In one experiment 28 of the forty respondents are classi ed as noncompensatory while none are classi ed as Dawes The remainder 72 could not be classi ed Broder s method is feasible for a small number of aspects 7 with four aspects the ratio of the largesttosmallest partworth in a noncompensatory model is based on 23 81 For the sixteen aspects as in our experiments the range of partworths in a noncompensatory model would be at least 215 32768 1 a ratio that puts severe strains on any statistical regres sionlike procedure1 We would like to develop a procedure that is more robust and can explain the data for more than 28 of the respondents Kohli and Jedidi 2004 propose a greedy heuristic to estimate a linear representation of lexicographic processes from metric conjoint data2 They modify Broder s procedure by com puting the number of violated pairs between predicted and observed rank orders for both additive and 21 models Their t statistics suggest that a 21 representation is not signi cantly different from an unconstrained additive model for 67 of the 69 respondents who evaluated pro les with ve features eleven aspects Our approach differs from Kohli and Jedidi 2004 along a number of dimensions including respondent task estimation algorithms and focus Nonetheless these parallel independent studies suggest many opportunities to apply discrete optimization methods to infer noncompensatory processes 3 The Respondent s Tasks It is easier to understand the Greedoid methods if we rst review the respondents task as illustrated with an example from our empirical experiments3 Respondents are rst introduced to the product category and the seven features sixteen aspects Figure 4a is one of many screens Respondents are then presented with SmartPhone pro les Figure 4b Respondents in the con siderthenrank cells simply click on those pro les they would seriously consider 7 part of the 1 The ratio is not as severe if we allow partial lexicographic orders However Broder s method cannot handle par tial orders without first solving the combinatorial problems we describe later 2 Both approaches were developed independently We became aware of one another s approaches after all empirical work had been completed and papers written Perhaps future research might modify each of the methods so that they might be compared on the same data 3 Greedoid analysis can be extended to tasks such as those used by Broder 2000 Gigerenzer and Goldstein 1996 or Gilbride and Allenby 2004 Gleeduldr ased Nunrcumpensaluvy lntetenee sereen ls shown m Flgure 4 These respondents then see only therr consldered pro les they are askedto rank thern by successlvely cllcklng on the pro le they would ehoose from the offered set Flgure 4d That pro le dlsappears and they ehoose agam unhl all conslderedproflles are ehosen an addtronal twrst Sorne butnot all respondents were allowedto presort the pro les m erther or both tasks A pnon we expeet the abrlrty to sort tasks to encourage lexlcographlc processlng 1n alater seetron we desenbe the full enpenrnental protoeol rneenhyes flller tasks holdout measures ete and provlde statrshes sueh as response rates Figured Illustrative Respondent39s Task cCunsldevallunJudgmemTask dChulceme CnnsldetallnnSel order Ftr tl Fltmtn h n n t tr n Sear n dl or that they p GreedoidBased Noncompensatory Inference 4 Identifying Best Lexicographic Fit with Greedoid Languages For ease of exposition we consider le 39 r39 39 orderings J by J by aspects ABA Eliminationbyaspects EBA can be estimated with the same algorithm by re defining aspects by their negation lexicographicbyfeatures LBF can be estimated by impos ing constraints on the aspect orders and lexicographicbyaspects can be estimated with only a slight modi cation in the algorithms To identify the best lexicographic representation from any partialordering data we de velop a procedure to identify the aspect order that maximizes t minimizes errors on some met ric Unfortunately as Martignon and Hoffrage 2002 Theorem 2 p 39 prove this problem is NPhard They suggest exhaustive enumeration For example they sought to determine the as pect order state capital soccer team in the national league etc that best explains the relative populations of two German cities Because their problem had nine aspects they needed to search 9 orderings 7 a UNIX machine took two days to nd the best ordering Their problem is a relatively small problem For our 4324 empirical problem exhaustive enumeration needs to check 7X43 orders for LBF l6 aspect orders for ABA or EBA and 216Xl6 orders for LBA4 Because 7X43 1929 7 their algorithm would have taken over a year per respondent for LBF Because 16 3003007X43 their algorithm would have taken over 300 millennia for ABA or EBA and substantially longer for LBA Although faster computers help it is clear that practical analysis for moderatetolarge problems requires a more ef cient algorithm We address computational ef ciency in two steps We rst demonstrate that a partial lexicographic ordering of m as they relate to a partial ordering of prof forms a Gree 5 This enables us to use established results to nd the appropriate lexicographic doid language aspect order if one exists much more efficiently than existing methods Because the pro le or dering need only be partial we can handle consideration partialrank fullrank or choice data A perfect lexicographic ordering of aspects is extremely rare With 32 pro les there are 32 rank orders but only 216Xl6 aspect orders Thus the chances that an arbitrary pro le order is consistent with an aspect order is less than 52 x 1018 Any respondent errors are likely to cause the data to be inconsistent with an aspect order6 Using the Greedoid structure we prove 4 In a 4324 design there are 3 X 4 4 X l 16 aspects 5 Our propositions are new to this paper Early theory examined partial orders Greedoids such as might be defined on orderings of profiles The Greedoid in this paper describes aspects as they relate to profiles not profiles directly 6 Interestingly less that 1103911 of 1 of the profile orderings are consistent with linear combination of aspect meas ures This includes both 1 and n n 39 39 39 J GreedoidBased Noncompensatory Inference that a dynamic program can nd the best ordering relative to a commonlyused goodnessof t metric The dynamic programming algorithm substantially reduces computation and makes it feasible to identify the best lexicographic ordering for large samples of respondents and moder ately large numbers of aspects For 16 aspects the dynamic program need only evaluate the or der of 216 65536 subsets of aspects much less than the 14 x 1018 potential LBA aspect or ders We begin with notation and de nitions Partial Orders and Consistency LetL L1 La be an ordered subset of a aspects where a S N For a given pro le P we let LiP be 1 if pro le P contains aspect Li and 0 otherwise We write P gt L P39 if LiP l and LiP39 0 where i is the rst index for which LiP 7E LiP39 Accordingly for each totally ordered setL of aspects there is a unique induced order of pro le preferences but the converse is not true In some cases there may be many different orders of aspects that lead to the same order of pro les This is particularly true for the consideration task 7 if a respondent will only consider Verizon SmartPhones that ip open then both the order Verizon ip and the order ip Verizon are consistent with the respondent s consideration process Suppose thatX is a partial order of pro les for a respondent For example X might de ne which pro les are in a consideration set and which are not orX might de ne a rankorder within the consideration set We write P gt X P39 if the respondent prefers Pro le P to Pro leP39 We say that an ordered subsetL of aspects is inconsistent with a partial orderX of pro les if there are pro les P and P39 such that P gt X P39 and P39 gt L P Otherwise we say thatL ananre consistent IfL is an ordered subset of aspects and ife e L is an aspect then L e is the ordered subset of aspects obtained by appending aspect e to the end of L Let LY denote the set L with all elements of Y deleted For example if L Verizon ip Palm operating system 6 Nokia and Y Palm operating system then L e Verizon ip Palm operating system Nokia and LY Verizon ip Greedoid Languages Greedoid languages were developed by Korte and Lovasz 1985 to study conditions un der which a greedy algorithm can solve optimization problems They have proven useful in se quencing and allocation problems e g Ni oMora 2000 We believe that this is the first appli GreedoidBased Noncompensatory Inference cation in marketing or consumer behavior Bjomer and Ziegler 1992 and Korte Lovasz and Schrader 1991 are excellent references that provide numerous examples of Greedoids In this work we introduce a new type of Greedoid where partial orders of X pro les induce a Gree doid language de ned on the aspects It is this linkage that enables us to identify LBA and other aspect or featurebased explanations of pro le orders LetE be a set of aspects let G be a collection of ordered subsets ofE let Q be the empty set and let the number of elements in a setL be denoted by 1L1 We say that G is a Greedoid lan guage if the following conditions are satis ed 1 Q e G 2 IfL e G and if element e e E is the last element ofL then Le e G 3 IfL e G and ifL e G and if lL l gt 1L1 then there is an element e inL 1 such that L L e and L e G In the appendix we demonstrate that partial orderings of the pro les form a Greedoid language on an aspect feature representation of the pro les Corollary 1 follows from Proposi tion 1 because Algorithm 1 is a greedy algorithm that either nds a consistent aspect order L e G of maximum length or terminates early7 Proposition 1 LetE be the set of aspects and letX be a partial order on the pro files Let G be the collection of ordered subsets of E that are lexico consistent withX Then G is a Greedoid language Corollary 1 Algorithm 1 determines whether there exists a lexicographic order ing of aspects L consistent withX and if an ordering exists nds an ordering Algorithm 1 for determining if X is lexicographic begin L Q while L is not a complete order of the aspect set E do begin if there is no aspect e of EL such that L e is consistent with X then quit because X is not lexicographic else choose an aspect e of EL for which L e is consistent withX and replace L by L e end end 7 Kohli and Jedidi 2004 use a greedy algorithm on permutation matrices to identify a metric representation of a lexicographic ordering when there is no response error They apply their algorithm to metric data 11 GreedoidBased Noncompensatory Inference Finding the Best Lexicographic Description Even if real respondents are attempting to use a noncompensatory rule they might make mistakes Alternatively the noncompensatory rule might only approximate their decision proc ess In either case we seek to nd the lexicographic ordering of aspects that best describes their partial order of pro les As a measure of t between aspects L and pro les X we relate closeness to the number of inconsistencies violated pairs between the pro le order induced by L and that observed in X 8 We now develop an algorithm to nd the closest lexicographic ordering Proposition 2 implies Algorithm 2 which is a dynamic program on the set of all sub sets of the aspects Because this set has dimensionality 2N and because 2N is substantially less than N Algorithm 2 can still be feasible when exhaustive enumeration is not In the appendix we prove Proposition 2 by showing that the marginal inconsistencies induced by adding a new aspect to an existing ordering depends only on that aspect and not on the prior orderings This implies a forward recursive structure which in turn implies dynamic programming Dynamic programming implies that the solution to Algorithm 2 is optimal This dynamic program is simi lar to the Held and Kalp s 1962 classic solution to the travelingsalesman problem For those readers not familiar with dynamic programming we provide a supplemental appendix available from the authors that illustrates how Algorithm 2 would apply to the playing card example in Figure 2 Proposition 2 LetL and L be two different permutations of the subsetE of aspects and let e be any aspect not in E Then the number of inconsistencies directly caused by e in L e is the same as the number ofinconsistencies caused by e in L e Corollary 2 Algorithm 2 identifies the best lexicographic description of a profile order X When the algorithm terminates JE is the minimum number of inconsistencies between the respondent s pro le ordering X relative to aspect set E LE is the best lexicographic or ders which may or may not be unique Algorithm 2 applies directly to either acceptanceby aspects or eliminationbyaspects Fortunately for lexicographicbyaspects the number of steps in the algorithm only doubles Speci cally in the innermost loop of Algorithm 2 we need only check both i and its negation We call Algorithm 2 a Greedoidbased dynamic program 8 Minimizing violated pairs is equivalent to maximizing Kendall s tau 1975 where 1 l 7 2fraction violated l2 GreedoidBased Noncompensatory Inference Algorithm 2 for nding L that is least inconsistent with X begin J 0 for k l to E for all unordered subsets S g E of size k for all i e S cSi i number of inconsistencies caused by aspect 1 following set Si next 1 JS IriisnJS 1 cS 11 LS is the ordering of aspects in S yielding JS retained next S next k end We have programmed Algorithm 2 in Java running on an IBM 17 GHz laptop For a 16 aspect problem the run time is approximately 185 seconds Relative to Martignon and Hoffrage 2002 some savings are due to Algorithm 2 and some are due to faster computers and pro gramming languages We project that Martignon and Hoffrage s exhaustive enumeration would take 14 years for a l6aspect EBA problem with Java on the same computer9 We provide two further results Proposition 3 extends the theory and Algorithms l and 2 to allow the researcher to place greater emphasis on some ordered pairs say the ordered pairs corresponding to highly ranked pro les Proposition 4 reduces the running time of Algorithm 2 by enabling it to begin with any consistent ordered subset of aspects e g the largest such or dered subset and then use the dynamic program on the remaining aspects Proposition 3 If weights are associated with each ordered pair inX then 1 the new G is a Greedoid language 2 Algorithm 1 determines whether there exists an L consistent withX 3 Proposition 2 extends to the new G and 4 Algorithm 2 nds the best lexico graphic description if c is redefined to cSi 1 sum of weighted violations caused by aspect ifollowing set Si 9 For LBA each lexicographic ordering includes all orientations ABA or EBA The number of solutions to check exhaustively would be 21616I Exhaustiver enumerating LBA would take over 900 millennia Exhaustiver enu merating a nineaspect problem would take 9 seconds for EBA or ABA but 13 hours for LBA l3 GreedoidBased Noncompensatory Inference Proposition 4 Suppose thotL is an ordering of a subset of aspects that is consistent with the preferences ofX Then there is an optimal ordering of aspects that begins with the order L 5 Benchmarks To evaluate the ability of the Greedoid methods to fit partialrank data and predict hold out validations we identify benchmark models To compare Greedoid analysis which is focused at the level of the individual respondent to a compensatory method also focused at the level of the individual respondent we use LINMAP Srinivasan and Shocker 1973 We obtain similar results for analytic center estimation Toubia et al 200410 Recent innovations enable data on the population rankings to inform individuallevel estimation via shrinkage For our data an appropriate shrinkage estimator is a hierarchical Bayes ranked logit model HBRL eg Rossi and Allenby 2003 These two benchmarks have proven accurate in practice and should provide an indication of the relative fit and predictive ability of Greedoid methods We seek to address two related but distinct issues First if the researcher is interested in developing a model to predict behavior then the appropriate benchmark is an unconstrained ad ditive model estimated with either LINMAP or HBRL Even though LBA and other lexico graphic models can be represented by additive models Greedoid methods might prove more ro bust for respondents who are truly lexicographic For example the additive representation for a 16 aspect problem requires partworths that differ by a ratio of as much as 32768l With such differences in true partworths and with respondent errors either LINMAP or HBRL may be less robust or more robust than the discrete Greedoid algorithm Behavioral researchers might also seek to identify whether compensatory or non compensatory models fit or predict observed choices best eg Broder 2000 Broder defines a respondent as compensatory if the respondent s partworths are not too extreme Specifically Broder requires that w wk for all Z i i where w is the partworth of the i3911 aspect for re spondent c We feel Broder s definition is too restrictive We define a respondent as q compensatory if w S qwlc for all Z i i If we set q l we obtain Dawes equal weights model as tested by Broder and if we set q gt 00 we obtain the unrestricted additive benchmark For 10 With large numbers of profiles eg 32 profiles analytic center estimation differs from LINMAP only by the er ror function that is minimized For our data the two methods differ by less than 1 on both fit and holdout predic tions Details from the authors GreedoidBased Noncompensatory Inference our empirical tests we set q 4 because simulation and empirical testing suggests that this set ting provides a reasonable compromise between the extremes of q l or q 00 The qualitative interpretations do not appear to depend on q We estimate these q compensatory benchmarks by imposing the appropriate constraint on the linear program and with rej ection sampling in the hi erarchical Bayes sampler We label these compensatory benchmarks LINMAPq and HBRLq Before addressing empirical data we wanted to establish that Greedoid methods and the various benchmarks perform well in their respective domains We generated synthetic respon dents with partworths by setting wm 2mm for the n3911 partworth Einhom s 1970 model Fol lowing Einhom m 0 implies Dawes model m 1 implies a minimally lexicographic model and 0 lt m lt l generates varying levels of compensatoryness Orderings of pro les were gen erated by adding normally distributed error to the sum of partworths Based on 32 ranked pro les from a 4324 design and based on 1000 synthetic respondents for varying levels of m we found that 1 when respondents were truly lexicographic Greedoid methods predict better than additive benchmarks 2 when respondents were truly qcompensatory the additive benchmarks fit better than Greedoid methods 3 when respondents were truly q compensatory knowledge of q improved estimation 4 in moderate ranges of m both the Greedoid methods and the bench marks provided comparable predictive ability and 5 predictive ability varied smoothly with q and m in the expected way Details are in a supplemental appendix available from the authors 6 SmartPhone Empirical Study To test Greedoid methods we invited respondents to complete a webbased questionnaire about SmartPhones The respondents were students drawn from the undergraduate and graduate programs at two universities To the best of our knowledge they were unaware of Greedoid methods or the purpose of our study As an incentive to participate they were offered a lin10 chance of winning a laptop bag worth 100 yielding a 63 response rate Pretests in related contexts suggested that SmartPhones were likely to include noncompensatory features and thus represented an interesting category for a first test of Greedoid methods and an interesting con trast to categories more likely to contain compensatory features The survey consisted of six phases The first three phases are as described in Figure 4 re spondents were introduced to the category and SmartPhone features indicated which Smart Phones they would consider in half the cells and successively chose SmartPhones in order to rank their considered products or rank all products depending on cell Respondents then com 15 GreedoidBased Noncompensatory Inference pleted a miniIQ test to cleanse memory 7 a task which pretests suggested was engaging and challenging Following this filler task respondents completed a holdout task consisting of two sets of four SmartPhones chosen randomly from a different 32profile fractional factorial de sign11 The final task was a short set of questions about the survey itself 7 data which we use to compare task difficulty For the holdout task in order to avoid unwanted correlation due to common measurement methods we used a different interface Respondents used their pointing device to shuf e the profiles into a rank order as one might sort slides in PowerPoint Pretests A that r J J J this task and found it different from the task in Figure 4d The survey was programmed in PHP and debugged through a series of pretests with 56 respondents chosen from the target population By the end of the pretests all technical glitches were removed Respondents understood the tasks and found them realistic Experimental Design Respondents were assigned randomly to experimental cells The basic experimental de sign is a 2X2 design in which respondents complete either a fullrank or a considerthenrank task and are given the opportunity to presort profiles or not Figure 5 In the considerthenrank sort cell respondents could sort prior to consideration w prior to choice Respondents in the sort cells could resort as often as they liked We also included an additional cell described below to test whether the results vary by the number of profiles presented to the respondents Figure 5 SmartPhone Experimental Design 32 Profiles in a 4324 Fractional Design ConsiderthenRank FullRank Cell 1 Cell 2 NO sorting 89 resps 82 resps consider 64 rank 32 Cell 3 Cell 4 Sorting allowed 87 resps 81 resps consider 6 7 rank 32 11 Future research might investigate the effect of wearout on lexicographic processing with cells that place the hold out tasks earlier in the survey GreedoidBased Noncompensatory Inference Task Difficulty Greedoid methods can be used to analyze any partialorder respondent task We rst eX amine whether the considerthenrank task is more natural and easier for respondents than the fullrank task The results are reported in Figures 6a and 6b We oriented both axes such that down is better We see rst that in the base condition of no sorting the considerthenrank task is seen as signi cantly more enjoyable accurate and engaging12 Sorting increases enjoyment accuracy and interest for the fullrank task but not for the considerthenrank task however nei ther difference is signi cant13 For the nosort cell twostage data collection saves substantial time 375 minutes compared to 875 minutes I 28p 001 Such time savings could reduce data collection costs substantially More respondents completed the nosort considerthenrank 94 than the nosort fullrank task 86 the difference is marginally signi cant t 17 p 010 However contrary to expectations sorting did not reinforce these attitude time and completionrate advantages In fact sorting appears to mitigate some advantages14 It appears that sorting as implemented was effortful and was perceived as such Figure 6 Task Difficulty less is better on both graphs 10 26 8 a 25 7 7 7 7 w 24 7 2 a 7 or a 5 7 E 23 7 5 4 7 m E E 22 7 3 7 D t 2 7 No Sun I Sorting I 2 1 7 No Sun I Sorting 1 7 L5 0 2 1 full rank consider hen rank full rank consider hen tank a Attitudes Toward Task Difficulty b Times to Complete the Tasks Predictive Ability We rst compare the most general Greedoid method LBA to the unconstrained additive 12 Comparing fullrank to considerthenrank I 22 p 003 for nosort cells I 09 p 037 for the sort cells 13 Comparing sort to nosort I 08 p 045 for considerthen rank cells I 06 p 053 for fullrank cells 14 The considerthen rank vs fullrank time difference is not significant for the sort cells I 04 p 070 The no sort vs sort time difference is not significant for the fullrank cells I 13 p 019 but is significant at the 010 level for the considerthen rank cells I 18 p 007 No other completion rate differences were significant 17 GreedoidBased Noncompensatory Inference models LINMAP and HBRL as averaged across respondents Holdout predictions are based on two metrics see Table 1 The percent of violated pairs provides more observations per respon dent 12 potential pairs from two sets of four ranked pro les but is precisely the metric opti mized by Greedoid methods and to some extent by LINMAP Hit rate provides fewer observa tions per respondent 2 and leads to more ties but is not optimized directly by either Greedoid methods or the benchmarks Empirically the two metrics are signi cantly correlated lt0001 level for all methods and provide similar comparative interpretations15 Table 1 Comparison of Fit and Prediction for Unconstrained Models Lexicographic by Hierarchical Bayes Ranked Logit L39NMAP Fit percent pairs 0955 0794 0793 Holdout percent pairs 0745 0693 0672 Holdout hit rate 0597 0499 0455 LBA significantly better than LINMAP and HBRL HBRL significantly better than LINMAP Tests at the 005 level Table 1 suggests that LBA predicts signi cantly better than the unconstrained bench marks on both holdout metrics and t Table 1 further con rms the advantage of shrinkage es timates for additive models HBRL vs LINMAP It appears that for these data Greedoid methods are more robust than the unconstrained additive models that could in theory t a leXi cographic process This apparent robustness is consistent with predictions by Mitchell 1997 and Martignon and Hot age 2002 p 31 and possibly due to the ratios of partworths 32768 1 that are necessary to t a lexicographic process for 16 aspects When we compare t at the individualrespondent level we see that there are no respon dents for whom HBRL ts better than LBA The more interesting comparison is for holdout predictions LBA predicts holdout pairs better than HBRL for 56 of the respondents worse for 40 of the respondents and is tied for 4 of the respondents We obtain similar insight from hit rates and for LINMAP16 Figure 7 provides a visual interpretation We plot a histogram of re 15 For example correlations are 070 for LBA 065 for HBRL and 068 for LINMAP Spear man s correlation also provides similar interpretations 16 For example for HBRL hit rates produce more ties 32 vs 4 For nontied respondents LEA is better on hit rates for 65 of the respondents and on holdout pairs for 59 of the respondents LBA vs LINMAP 65 better and 3 tied for holdout pairs 55 better and 17 tied for hit rate 18 GreedoidBased Noncompensatory Inference spondents versus the difference in predictive ability between the two models Positive numbers shown in dark red indicate the respondents for whom LBA predicts better Figure 7 Histogram of Comparative Predictive Ability 04 03 02 01 0 0 01 02 03 04 05 06 07 Difference in Percent Pairs Predicted Noncompensatory vs Compensatory Processes We next examine whether respondents are best described as noncompensatory or com pensatory Three comments are in order First this description is paramorphic We say only that respondents rank choose consider pro les they were following one or the other proc ess Second we have some con dence in the descriptions because LBA predicts better for syn and a thetic r J whoarele39 rquot J additive model qcompensatory predicts better for synthetic respondents who are qcompensatory Third for comparison we use the better of the two qcompensatory models HBRL4 for simplicity of exposition Table 2 compares LBA to the qcompensatory models On average LBA predicts and ts signi cantly better than the qcompensatory models At the level of the individual respon dent based on holdout pair predictions LBA predicts better for 65 of the respondents HBRL4 predicts better for 44 and l are tied For hit rates the percentages are 52 21 and 28 Hit rates provide less discriminant ability because most values are 0 12 or 1 for two holdout sets of four profiles Table 2 and the holdout predictions suggest that a signi cant frac tion of respondents behave as if they were using a decision process that is better represented by a lexicographic than a qcompensatory process GreedoidBased Noncompensatory Inference Table 2 Comparison of Fit and Prediction for qCompensatory Models and LBF Hierarchical Lex39 gfg gc by Bayes Ranked LINMAP q 4 Lex39gggiifehs39c by p Logit q 4 Fit percent pairs 0955 0731 0697 0826TT Holdout percent pairs 0745 0655 0626 0658T Holdout hit rate 0597 0431 0382 048 1T LBA significantly betterthan LINMAP4 HBRL4 and LBF HBRL4 significantly betterthan LINMAP4 TTLBF significantly better than HBRL4 and LINMAP4 TLBF significantly better than LINMAP4 All tests at the 005 level Constructed Processes D 39 39 39 39 1 1 i that construct their decision processes as they make their decisions and hence that these decision processes can be in uenced by the na ture of the decision task We examine this issue by comparing the in uence of task consider thenrank vs fullrank and the availability of a presorting mechanism sorting allowed vs not allowed Figure 8 compares the predictive ability holdout violations for the four cells of our basic experiment Some insights from Figure 8 are17 0 LBA predicts better than a qcompensatory model in all cells and signi cantly better in all but the considerthenrank nosort cell LBA predicts better for the fullrank cells than for the considerthenrank cells Fur thermore LBA predicts better for 76 of the respondents in the fullrank cells vs 56 in the considerthenrank cells However this observation is tempered with the realization that the fullrank cells provide more ordered pairs than the considerthenrank cells 496 vs 183 on average 0 Neither LBA nor HBRL4 predicts signi cantly better or worse when sorting is allowed We obtain a similar pattern of results for hit rates with the exception that HBRL4 has a signi cantly lower hit rate for the fullrank nosortvssort cells I 21 p 00318 17 t values pvalues for LBA vs HBRL4 are 13 021 73 000 21 04 50 000 for Cells 14 For rank vs considerthen rank they are 57 000 and 44 000 for no sort and sort LBA and 04 072 and 08 040 for no sort and sort HBRL4 For nosortvssort they 06 057 and 14 015 for considerthen rank and rank LBA and 10 031 and 02 084 for considerthen rank and rank HBRL4 18 Hitrate t values pvalues for LBA vs HBRL4 are 14 018 66 000 27 01 34 000 for Cells 14 For rank vs considerthen rank they are 30 000 and 24 000 for no sort and sort LBA and 19 053 and 13 020 20 GreedoidBased Noncompensatory Inference Figure 8 Predictive Ability by Cell Lexicographic vs qCompensatory Processes 09 09 E 08 7 08 7 g m E E 7 8 07 7 07 E II I g 06 7 g 06 7 m 05 7 I 05 0 4 04 full rank consider then rank fun rank cansme39 thequot tank a No Sorting Allowed b Sorting Allowed We assigned an additional 86 respondents to a fifth cell in which they evaluated fewer profiles 16 vs 32 with the considerthenrank task Behavioral theory suggests that respon dents are more likely to use a lexicographic process if there are more pro les eg Bettman Luce and Payne 1998 Johnson Meyer and Ghose 1989 Lohse and Johnson 1996 Payne Bett man and Johnson 1993 However we found no signi cant differences in holdout predictions pairs or hit rate suggesting that the number of pro les did not affect the relative predictive abil ity of LBA and HBRL4 Because earlier experiments were based on moreintrusive meas ures future research might examine whether that measurement in part induced the observed in crease in the use of noncompensatory processes If applications in other categories con rm that the relative predictive ability does not depend on the number of pro les then researchers might nd it more convenient and easier on J to study 1 n r y r 39 with fewer pro les20 Researchers also might nd that 16 pro les are suf cient to trigger non compensatory processing In summary for SmartPhones contrary to intuition and prior research it appears that nei ther sorting nor increasing the number of pro les induced more lexicographic processing How for no sort and sort HBRL4 For nosortvssort they 01 092 and 06 058 for considerthen rank and rank LBA and 11 027 and 21 003 for considerthenrank and rank HBRL4 19 t values pvalues for 32 vs l6profiles are 03 098 and 00 035 for LBA and HBRL4 holdout pairs They are 09 036 and 07 046 for LBA and HBRL4 hit rates Comparing the classification to LBA vs HBRL4 they are 09 032 18 007 and 18 007 for fit holdout pairs and hit rate 20 There was a significant increase in enjoyment and interest I 20 p 005 but no significant decrease in task time I 05 p 064 for this considerthen rank task 21 GreedoidBased Noncompensatory Inference ever it appears that task format difficulty full rank vs considerthenrank might have induced lexicographic processing Aspects vs Features As a nal behavioral question we address whether respondents process pro les by fea tures or by aspects when they use lexicographic processes Recall that lexicographicbyfeatures LBF is a restricted form of LBA where respondents rank by features eg Verizon vs Sprint vs Nextel vs Cingular rather than aspects Verizon vs notVerizon Because LBA is the more general model its m statistics will be better However there is no guarantee that LBA s holdout predictions will be better than those of LBF If respondents process pro les by features then LBF should predict as well as LBA perhaps better if LBA exploits random variations Table 2 compares LBA to LBF On average LBA predicts signi cantly better on both holdout Violations and hit rates LBA predicts better in all four cells and signi cantly better in three ofthe four cells t s 18 71 24 and 45 p s 007 000 002 and 000 in Cells l4 However LBF predicts better for about a third of the respondents 35 holdout Violations and 34 hit rate no signi cant differences between experimental cells 7 Analysis of Computer Data from a Study by Lenk et al 1996 We chose SmartPhones for our initial study because a priori we expected some features aspects to be noncompensatory We were fortunate to obtain a classic conjointanalysis data set in which respondents evaluated full pro les of computers that varied on thirteen binary fea tures telephone service hot line amount of memory screen size CPU speed hard disk size CD ROM cache color availability warranty bundled software guarantee and price Respondents were presented with 16 full pro les and asked to provide a rating on a 10point likelihoodof purchase scale They were then given a holdout task in which they evaluated four additional pro les on the same scale These data were collected and analyzed by Lenk et al 1996 who suggest excellent t and predictive ability with hierarchical Bayes compensatory models Based on their analysis and our intuition we felt that the features in this study were more likely to be compensatory than those in the SmaltPhone study However this is an empirical question We rst degraded the data from ratings to ranks For example if Pro le A were rated as a 10 and Pro le B were rated as a l we retained only that Pro le A was preferred to Pro le B Because there were 10 scale points and 16 pro les there were many ties 7 an average of 66 unique ratings per respondent Interestingly even though there were many ties there were ap 22 GreedoidBased Noncompensatory Inference proximately 96 ranked pairs of pro les per respondent 7 80 of what would be obtainable with full ranks Because the degraded data are partial ranks we can analyze the data with Greedoid methods and compare predictions to HBRLoo and HBRL4 Table 3 reports the t and prediction results for the computer data As with the Smart Phone data we address 1 predictive ability compared to an unconstrained additive model and 2 the relative predictability of LBA and a qcompensatory model On these data the uncon strained additive model predicts better than LBA signi cantly so on holdout pairs The differ ence in hit rates is one respondent in 201 Interestingly LBA on the degraded data does as well as m hierarchical Bayes on the ratings data 0687 Lenk et al p 181 and better than ei ther OLS 0637 ibid and latent class analysis 0408 ibid21 Table 3 is consistent with the analysis of metric data by Jedidi and Kohli 2004 who found that a different lexicographic model binary satis cing LBS t almost as well as an un constrained additive model 093 t pairs for LBS vs 095 for LINMAP no data available on holdouts The JedidiKohli context is remarkably similar to that of Lenk et al metric ratings of 16 laptop computers described by memory brand CPU speed hard drive size and price in a 3322 fractional design Table 3 Comparison of Fit and Prediction for Computer Data Lenk et al 1996 Lexicographic by Hierarchical Bayes Hierarchical Bayes Aspects Ranked Logit Ranked Logit q 4 Fit percent pairs 0899 0906 0779 Holdout percent pairs 0790 0827 0664 Holdout hit rate 0686 0692 0552 HBRL significantly better than LBA and HBRL4 LBA and HBRL significantly better than HBRL4 at 005 level We also address classi cation by either LBA or a qcompensatory model For the com puter data LBA predicts better for 58 of the respondents compared to 25 for HBRL4 the remainder are tied We distinguish fewer respondents by hit rate because hitrate classi cation is a highervariance classification 32 LBA 20 HBRL4 and 47 tied 21 We compare to the highest hit rate they report 7 that for HB estimated with 12 profiles For 16 profiles they re port a hit rate of 0670 For other statistics HB with 16 profiles performs better than with 12 profiles ibid p 181 23 GreedoidBased Noncompensatory Inference Comparing the SmartPhone and computer data we get a surprisingly similar respondent level comparison of lexicographic and qcompensatory models If we consider only the nontied respondents LBA predicts better than HBRL4 for 66 of the SmartPhone respondents and 70 of the computer respondents22 Jedidi and Kohli 2004 did not test a qcompensatory model but they did nd that an unconstrained additive model was not signi cantly different from LBS for 67 of their respondents Thus on all data sets about 2 of 3 respondents might be described as using a lexicographic process Comparing LBA vs an unconstrained additive model HBRL there are some differences between the data sets For SmaltPhones LEA is signi cantly better for both holdout pairs 75 vs 69 and hit rates 60 vs 50 For computers LEA is comparable on hit rates 69 vs 69 but not as good on holdout pairs 79 vs 83 These differences might be explained by the differences in the data sets The data sets differ on context computers vs SmartPhones de pendent measures ratings vs rankings and the number of aspects 13 vs 1623 The latter is not trivial because lexicographic partworths imply ratios of 2N391 ie 1024l for laptop com puters 4096l for computers and 32768l for SmartPhones Our best guess is that the nature of the product categories is the prime cause of the differences but further investigation on other data is warranted In both cases we are encouraged by the relative predictability of LBA a pre dictive ability that might improve as the respondent tasks are re ned in future studies 8 Managerial Implications Manufacturers retailers or website designers seek to design products store layouts or websites that have or emphasize those aspects that customers use to accept products for further consideration They seek to avoid those aspects that customers use to eliminate products In the parlance of product development these are the musthave or mustnot have aspects or fea tures Hauser Tellis and Grif n 2005 Both General Motors and Nokia have indicated to us that the identi cation of musthave aspects is an extremely important goal of their product development efforts private communication Table 4 lists the six aspects that were used most often and indicates whether they were used to accept pro les or reject pro les second column the percent of consumers who used that aspect as one of the first three aspects in a lexicographic 22 The corresponding percentages for hit rates are 71 and 61 23 The computer data are based on 16 profiles rather than 32 but our fifth cell suggests that this difference does not induce significantly more lexicographic processing Nonetheless behavioral theory suggests that it might 24 GreedoidBased Noncompensatory Inference order third column and the percent who used that aspect as the first aspect in a lexicographic order fourth column Table 4 has a number of implications Firstly for our student sample there are clear price segments 7 almost half the sample rejected highpriced SmartPhones Secondly the as pects of ip and small are each used by about 30 of the respondents For this sample any manufacturer will lose considerable market share if it did not include SmartPhones that are small and ip The keyboard aspect is interesting One segment 173 seems to require a keyboard and another segment 75 not shown seems to reject all keyboard SmartPhones On this as pect a manufacturer would be best advised to offer both SmartPhones with keyboards and SmartPhones without keyboards Finally brand service provider and operating system are not high in the lexicographic ordering It is interesting that in our data price aspects were often but not always rejection crite ria while all other aspects were acceptance criteria This is true for aspects not shown in Table 4 We do not know if this generalizes to other categories Furthermore although highprice was the top lexicographic aspect in our study this may be a consequence of the category or our student sample We do not expect price to be the top lexicographic aspect in all categories nor do we feel that this result affected the basic scientific and methodological findings about lexico graphic processing or predictive ability Top Lexicographic Aspectslfielgr iiartPhones for our sample Aspect ABA or EBA Affect Considerationquot Top Aspectf Price 499 Reject 492 261 Flip Accept 320 104 Small Accept 294 100 Price 299 Reject 198 42 Keyboard Accept 173 75 Price 99 Accept 145 48 Column sums to 300 over all aspects TColumn sums to 100 across all aspects Some aspects not shown 9 Summary Conclusions and Future Research In this paper we propose methods to estimate noncompensatory process descriptions with either rank or partialrank data Estimation is a nontrivial combinatorial problem which 25 GreedoidBased Noncompensatory Inference has hitherto been too timeconsuming to solve Greedoids provide a structure and theory to transform an N problem into a 2N problem which for practical problems decreases running time by a factor the order of 1013 We tested the new methods empirically for SmartPhones and computers Consistent with simulations the data suggest that Greedoid methods can estimate lexicographic models that pre dict well Signi cant fractions of respondents about 2 of 3 appear to process profiles lexico graphically by either aspects or features Greedoid methods enable us to examine the impact of sorting the number of profiles and the respondent s task Greedoid methods are exible We tested the methods with fullrank considerthenrank and degraded ratings tasks but the methods apply to any partialorder task including repeated choice tasks The considerthenrank task saves time increases completion rates and is per ceived by respondents as more enjoyable more accurate and more interesting Because Gree doid methods predict better than compensatory models on SmartPhones and as well or almost as well on computers Greedoid methods are a promising new method for product development and market simulators In summary based on the simulations the SmartPhone data and the computer data Methodological o it is feasible to estimate noncompensatory processes with a Greedoid dynamic program 0 a considerthenrank task reduces task time increases completion rates and improves perceived enjoyment accuracy and interest however at some loss in predictive ability 0 enabling respondents to sort profiles by aspects is seen as more difficult and time consuming but does not increase predictive ability 0 noncompensatory estimates predict holdouts well 0 Greedoid methods appear to be robust 7 they predict well even though additive models can represent lexicographic processes Consumer Behavior 0 compared to a q compensatory model more respondents appear to be using non compensatory models 0 more respondents appear to process aspects rather than features lexicographically 26 GreedoidBased Noncompensatory Inference enabling respondents to sort pro les does not increase their tendency to use non compensatory processes increasing the number of pro les does not increase respondents tendency to use non compensatory processes the fullrank task does increase lexicographic processing relative to the considerthen rank task Managerial for our sample and category 0 Price is often used as a rejection criterion Nonprice aspects seem to be used as accep tance criteria 0 Small and Flip are key acceptance criteria for SmartPhones Future Directions Greedoid methods provide a promising tool to study consumer behavior Researchers can use the Greedoid inference engine to investigate many impacts of consumers constructive judgment and decision processes 7 manipulations that might be too intrusive if implemented by verbal protocols or information display tasks Methodologically the exact dynamic program is still exponential in the number of as pects We handled l6 aspects in 185 seconds At this rate Greedoid methods can be used to evaluate up to 21 aspects in under a minute However we can handle much larger problems if we seek to concentrate on the rst few lexicographic aspects in a respondent s LBA process Because the theory applies to partial orders we can stop the dynamic program afterM aspects yielding a running time proportional to NCM For example we could identify the top ve out of fty aspects in approximately one minute Partialorder Greedoid methods can be used to iden tify satis cing processes in which some aspect levels are considered as equivalent by respon dents Other heuristics might also be used Kohli and Jedidi 2004 Kohli Krishnamurthi and Jedidi 2003 Finally there are interesting commonalities and differences between the SmartPhone and computer data sets and perhaps some empirical generalizations 27 GreedoidBased Noncompensatory Inference References References Abernethy Jacob Theodoros Evgeniou and J eanPhilippe Vert 2004 An Optimization Framework for Adaptive Questionnaire Design INSEAD Fontainebleau FR Batra Rajeev John G Myers and David A Aaker 1996AdvertisingManagernent 5E Englewood Cliffs NJ PrenticeHall Inc Bettman James R Mary Frances Luce and John W Payne 1998 Constructive Consumer Choice Processes Journal ofConsurner Research 25 3 December 187217 and L W Park 1980 Effects of Prior Knowledge and Experience and Phase of the Choice Process on Consumer Decision Processes A Protocol Analysis Journal of Consumer Research 7 234 248 Broder Arndt 2000 Assessing the Empirical Validity of the Take the Best Heuristic as a Model of Human Probabilistic Inference Journal of Experimental Psychology Learning Memory and Cognition 26 5 13321346 Chase Valerie M Ralph Hertwig and Gerd Gigerenzer 1998 Visions of Rationality Trends in Cog nitive Sciences 2 6 June 206214 Dawes R M 1979 The Robust Beauty of Improper Linear Models in Decision Making Arnerican Psychologist 34 571582 Dawkins Richard 1998 Unweaving the Rainbow Science Delusion and the Appetite for Wonder Boston MA Houghton Mif in Company DeSarbo Wayne S Donald R Lehmann Greg Carpenter and I Sinha 1996 A Stochastic Multidi mensional Unfolding Approach for Representing Phased Decision Outcomes Psychometrica 61 September 485508 Einhorn Hillel J 1970 The Use of Nonlinear Noncompensatory Models in Decision Making Psy chological Bulletin 73 3 221230 and Robin M Hogarth 1981 Behavioral Decision Theory Processes of Judgment and Choice Annual Review of Psychology 32 5288 Fishburn Peter C 1974 Lexicographic Orders Utilities and Decision Rules A Survey Managernent Science 20 11 Theory July 14421471 Frederick Shane 2004 Cognitive Impulsivity and Decision Making Working Paper MIT Sloan School of Management Cambridge MA 02142 Under review Journal of Economic Perspec tives Gensch Dennis H 1987 A Twostage Disaggregate Attribute Choice Model Marketing Science 6 Summer 223231 and Ehsan S Soofr 1995 InformationTheoretic Estimation of Individual Consideration Sets In ternational Journal of Research in Marketing 12 May 2538 28 GreedoidBased Noncompensatory Inference References Gigerenzer Gerd and Daniel G Goldstein 1996 Reasoning the Fast and Frugal Way Models of Bounded Rationality Psychological Review 1003 4 650669 Gilbride Timothy and Greg M Allenby 2004 A Choice Model with Conjunctive Disjunctive and Compensatory Screening Rules Marketing Science 23 3 Summer 391406 Green Paul E Abba M Krieger and Pradeep Bansal 1988 Completely Unacceptable Levels in Con joint Analysis A Cautionary Note Journal ofMarketing Research 25 August 293300 Grif n Abbie and John R Hauser 1993 quotThe Voice of the Customerquot Marketing Science vol 12 No 1 Winter 127 Hauser John R 1978 quotTesting the Accuracy Usefulness and Significance of Probabilistic Models An Information Theoretic Approachquot Operations Research Vol 26 No 3 MayJune 406421 Gerald Tellis and Abbie Grifm 2005 Research on Innovation A Review and Agenda for lVIarketing Science forthcoming Marketing Science and Birger Wernerfelt 1990 quotAn Evaluation Cost Model of Consideration Setsquot Journal of Consumer Research Vol 16 March 393408 Held M and R M Karp 1962 A Dynamic Programming Approach to Sequencing Problems SIAM Journal oprpliealMathernatics 10 196210 Jedidi Kamel and Rajeev Kohli 2004 Probabilistic SubsetConjunctive Models for Heterogeneous Consumers Working Paper Graduate School of Business Columbia University November and Wayne S DeSarbo 1996 Consideration Sets in Conjoint Analysis Journal ofMarket ing Research 33 August 364372 Johnson Eric J and Robert J Meyer 1984 Compensatory Choice Models of Noncompensatory Proc esses The Effect of Varying Context Journal of Consumer Research 11 1 June 528541 and Sanjoy Ghose 1989 When Choice Models Fail Compensatory Models in Negatively Correlated Environments Journal ofMarketing Research 26 August 255290 Johnson Richard 1991 Comment on Adaptive Conjoint Analysis Some Caveats and Suggestions Journal ofMarketing Research 28 May 223225 Kendall Maurice G 1975 Rank Correlation Methods London England Charles Grif n amp Company Ltd Kim J in Gyo 2004 Dynamic Heterogeneous Choice Heuristics A Bayesian Hidden Markov Mixture Model Approach Working Paper MIT Sloan School of Management Cambridge MA Klein Noreen M 1988 Assessing Unacceptable Attribute Levels in Conjoint Analysis Aalvances in Consumer Research vol XIV pp 154 15 8 Kohli Rajeev and Kamel J edidi 2004 Representation and Inference of Lexicographic Preference Models and Their Variants Working Paper Columbia University New York NY December 29 GreedoidBased Noncompensatory Inference References Ramesh Krishnamurthi and Kamel Jedidi 2003 SubsetConjunctive Rules for Breast Cancer Di agnosis Graduate School of Business Columbia University May Korte B and L Lovasz 1985 Basis Graphs of Greedoid and Twoconnectivity Mathematical Pro gramming Study 24 158165 Lenk Peter J Wayne S DeSarbo Paul E Green and Martin R Young 1996 Hierarchical Bayes Con joint Analysis Recovery of Partworth Heterogeneity from Reduced Experimental Designs Marketing Science 15 2 173191 Lohse Gerald J and Eric J Johnson 1996 A Comparison of Two Process Tracing Methods for Choice Tasks Organizational Behavior and Human Decision Processes 68 1 October 2843 Luce Mary Frances John W Payne and James R Bettman 1999 Emotional Tradeoff Dif culty and Choice Journal ofMarketing Research 36 143159 Malhotra Naresh 1986 An Approach to the Measurement of Consumer Preferences Using Limited In formation Journal ofMarketing Research 23 February 3340 Martignon Laura and Ulrich Hoffrage 2002 Fast Frugal and Fit Simple Heuristics for Paired Com parisons Theory and Decision 52 2971 Mitchell Tom M 1997 Machine Learning Boston MA WCB McGrawHill Montgomery H and O Svenson 1976 On Decision Rules and Information Processing Strategies for Choices among Multiattribute Alternatives Scandinavian Journal of Psychology 17 283291 Nakamura Yutaka 2002 Lexicographic Quasilinear Utility Journal of Mathematical Economics 37 5 7 178 Ni oMora Jose 2000 quotOn Certain Greedoid Polyhedra Partially Indexable Scheduling Problems and Extended Restless Bandit Allocation Indicesquot Economics Working Papers 456 Department of Economics and Business Universitat Pompeu Fabra Ogilvy David 1985 Ogilvy on Advertising New York NY Vintage Books Olshavsky Richard W and Franklin Acito 1980 An Information Processing Probe into Conjoint Analysis Decision Sciences 11 July 451470 Oppewal Harmen Jordan J Louviere and Harry J P Timmermans 1994 Modeling Hierarchical Con joint Processes with Integrated Choice Experiments Journal of M arketing Research 31 Febru ary 92 10 5 Payne John W 1976 Task Complexity and Contingent Processing in Decision Making An Informa tion Search Organizational Behavior and Human Performance 16 366387 James R Bettman and Eric J Johnson 1988 Adaptive Strategy Selection in Decision Making Journal of Experimental Psychology Learning Memory and Cognition 14 534552 and Eric J Johnson 1993 T heAalaptive Decision Maker Cambridge UK Cambridge Uni versity Press 30 GreedoidBased Noncompensatory Inference References Reeves Rosser 1961 Reality in Advertising New York NY Knopf Publishing Roberts John H and James M Lattin 1991 Development and Testing of a Model of Consideration Set Composition Journal ofMarketing Research 28 November 429440 Rossi Peter E and Greg M Allenby 2003 Bayesian Statistics and Marketing Marketing Science 22 3 Summer 304328 Shugan Steven M 1980 The Cost of Thinking Journal of Consumer Research 7 2 September 99 11 1 Srinivasan V and Chan Su Park 1997 Surprising Robustness of the SelfEXplicated Approach to Cus tomer Preference Structure Measurement Journal ofMarketing Research 34 May 286291 and Allan Shocker 1973 Linear programming Techniques for Multidimensional Analysis of Pref erences Psychometrika 38 3 September 337369 and Gordon A Wyner 1988 Casemap ComputerAssisted SelfEXplication of Multiattributed Preferences in W Henry M Menasco and K Takada Eds Handbook on New Product Devel opment and Testing Lexington MA D C Heath 91112 Swait Joffre 2001 A Noncompensatory Choice Model Incorporating Cutoffs Transportation Re search 35 Part B 903928 Thomgate W 1980 Ef cient Decision Heuristics Behavioral Science 25 May 219225 Toubia Olivier Duncan 1 Simester John R Hauser and Ely Dahan 2003 Fast Polyhedral Adaptive Conjoint Estimation Marketing Science 22 3 Summer 273303 Tversky Amos 1972 quotElimination by aspects A theory of choicequot Psychological Review 79 281299 Urban Glen L and John R Hauser 2004 ListeningIn to Find and Explore New Combinations of Customer Needs Journal ofMarketing 68 April 7287 Zaltman Gerald 1997 Rethinking Market Research Putting People Back In Journal of M arketing Research 23 November 424437 31 GreedoidBased Noncompensatory Inference Appendix Appendix Proofs of the Formal Propositions Proposition 1 LetE be the set of aspects and letX be a partial order on the pro les Let G be the collection of ordered subsets of E that are lexico consistent withX Then G is a Greedoid language Proof We show that Greedoid properties 2 and 3 hold for collection G Property 1 is implied by 2 Property 2 Lexico consistent means that there is no pair of pro les P and P39 with P gt L P39 and P39 gt X P So ifL is consistent with X then Le is consistent witthince the relations with respect to Le are a subset of the relations with respect to L Property 3 Let e be the rst aspect in L39 such that e e L Such an e is guaranteed to exist since lL39l gt L We show that L e e G Via a contradiction Suppose that there are pro les P and P39 withP gt172 P39 and P39 gt X P Since L andX are consistent it follows that P and P39 are unrelated with respect to L and thus P gt Z P39 Let Lquot be aspects in L39 prior to e Then Lquot g L soP and P39 are unrelated in Lquot It follows that P gt1 P39 and thus P gt L P39 contradicting that L39 is consistent with X We conclude that Property 3 is true Proposition 2 LetL and L be two difkrent permutations of the subsetE of aspects and let e be any aspect not in E Then the number of inconsistencies directly caused by e in L e is the same as the number ofinconsistencies caused by e in L e Proof Suppose that for pro les P and P39 P gt X P39 The aspect e causes an inconsis tency with respect to the pro les P and P39 in L e if and only if the following conditions hold i pro les P and P39 are undifferentiated by the aspects in L and ii P39 gt Z P These are the same conditions under which e causes an inconsistency with respect to P and P39 in L e Proposition 3 If weights are associated with each ordered pair inX then 1the new G is a Greedoid language 2 Algorithm 1 determines whether there exists an L consistent withX 3 Proposition 2 extends to the new G and 4 Algorithm 2 finds the best lexicographic description ifc is redefined to cSi i sum ofweights ofviolations caused by aspect ifollowing set Si Proof Proposition 1 and Algorithm 1 are unaffected by nonunit weights because the de termination of consistency does not depend on the weights associated with inconsistencies Proposition 2 extends easily to the case where nonunit weights are allowed With essentially the same proof it can be shown that the sum of the weights of inconsistencies directly caused by as pect e in order L e is still independent of the permutation of the preceding aspects L With the rede nition of cSi i the validity of the new dynamic programming formulation follows from the extension of Proposition 2 32 UP 269 Professor Hecht Wednesday25 Spring 2008 Rural Development Peasants and Development Old debates New Theory Different World While peasants still constitute about half of the world s population their role has shifted dramatically one might say from an agent of history think Mexican Russian Chinese Cuban Vietnamese etc revolutionsrather to its victims Or have they This course reviews some of the classic literatures on peasantries and outlines some of the central debates about rural development peasants politics resistance and their future To do so we analyze the historical views of peasantries how these have changed over time and how their positions in the developing economies have changed In a central way development policy increasingly places them as marginal economic actors while environmental concerns place peasants at the heart of resource stewardship Other factors such as technical change in agriculture cyclic outmigration and new forms of labor organization have raised questions about land redistribution peasant politics about the gender division of labor identity a range of broader implications Finally the way of thinking about peasants and the way they think about themselves has also changed and is more deeply imbued with questions of identity and capacities in rural development Peasant revolutions transformed the political world of the 20Lh century with the revolutions in Mexico China Russia Vietnam Cuba and Central America and continue to reshape the political landscape in sharply divergent ways from the Zapatistas to Zimbabwe What is going on Course requirements Do the reading An exercise take a l9Lh century explorer literature that focuses on the area you are interested and compare in to a contemporary at least late 20Lh cent description of the same area You have to analyse the kind of ideas and ideologies that inform how they are viewed Take one of the novels and review it through the materials of the class Books for the course are None are in the bookstore yet which did a great job of the novels Scott J 1985 Weapons of the Weak New Haven Yale Davis M 2000Vict0139ian H010caustsLondon Verso Fox J 2006 Accountability Politics Power and Voice in Rural Mexico Oxford Press Kearney R 1996 Reconceptualizing the Peasantry Boulder Westview Collier G Basta Land and Rebellion in Chiapas Optional Wolf E 1978 Peasant wars of the 20th Century U Okla Press Robbins P 2005 Political Ecology New York Blackwell Great Novels Memoires of Peasantries and Rebellion Da Cunha 1897 Rebellion I n the Backlands U Chicago Press Zola E Germinal Penguin Menchu R I Rigoberta Menchu Verso Week One The general introduction Section I The Peasant Economy What do we mean Week Two What is a Peasant From Ethnography to Political Ecology From Closed to Global Economy Some questions about Culture and the Rural Pratt ML 1985 Scratches on the Face of the Country Critical Inquiry 12119142 Reader Kearney M 1996 Chapters Kinds of Others in the History of Anthropology Peasants and antimonies of the Modern State Reconceptualizing the Peasantry Westwood Week Three Big Debate 1 The Peasant as a Separate Economy or Class Does it matter and why The populist debate Chapters from Chayanov Theory of the Peasant Economyon reserve Look also Kerblay and Thorner s essays in this volume Scott J Selections Moral Economy of the Peasant New Haven Yale reader Scott J Part 1Weapons of the Weak Chaps 1 and 2 The Class debate Lenin V 1899 quotThe Differentiation of the Peasantryquot reader Bernstein H African peasantries Journal of Peasant Studies reader De Janvry and CD Deere A Conceptual framework for the analysis of peasants American Journal of Agri cultural F 39 Reader Understanding Agrarian Transitions and what they mean prelude to modernism Week Four Agrarian Transitions then and now Modalities of enclosure Questions of changes in tenurial regimes access regimes dispossession and power relations Davis M Victorian Holocausts from peasant to debt peon in the 19Lh century Part III Deciphering ENSO and Climates of Hunger Part 11 El Nine and the New Imdperialism Chapter 9 the origins of the 3r World Kearney Chap 4 Romantic Reaction to modernist peasant studies Bryant R 1994 Shifting the Cultivator Modern Asian Studies 282 225250 Robbins Chapter 3 the Essential Tools Big Themes in Peasant literatures Post WWII ISI and the Modernization of Agriculture Green revolutions and early ideological globalizations Week Five Agrarian Transitions and What They Mean Modernization and its malcontents The questions of internal changes in production Look at Collier and Basta Scott Weapons of the Weak Chapters 34 5 6 Kearney Romantic reactions to the Modernist peasant Studies Hecht S B 1985 Environment Development and Politics Capital Accumulation and the Livestock Sector in Eastern Amazonia World Development 13 6663684 De Janvry Disarticulated Accumulation Reader Week Six Kearney Social Fields of Identity and Politics What about Women Folbre N 1986 Hearts and spades Paradigms of Households Economics World Development Reader R Schroeder and K Suryanata 1997 Gender and class power in Agroforestry systems Deere CD 2003 Women s land rights and social movements in the Brazilian Agrarian Regime Journal of Agrarian Change Pearson R and Jackson 1998Feminism Gender and Policy IN Feminist Visions of Development Routledge reader Hamilton S 2002 Neoliberalism gender and property rights in rural Mexico Latin American Research Review 37 1 1 19143 Week Seven Peasantries Agrarian Transitions and the Questions of Nature Bray D B E A Ellis N ArmijoCanto and C T Beck 2004 The institutional drivers of sustainable landscapes a case study of the Mayan Zone in Quintana Roo Mexico Land Use Policy 21 4333346 Leach M Meams and Scoones 1999 Environmental Entitlements World Development Vol 272 225247 Raf es H 1999 Local theory nature and the making of an Amazon Place Cultural Anthropology 143 323360 Neumann R 2004 Nature State territory In Peet and Watts Liberation Ecology Scoones I 1999 New ecology and the Social Sciences Ann Rev of Anthropology 28479507 Scan Political Ecology Chapters Destruction of nature Construction of nature Week Eight Peasants and Land reform and the inventions of identity Post Colonialism and other question Bernstein H 2002 Land Reform taking the Longer View Journal of Agrarian Change Vol 24 433463 Brass T 2005 Neoliberalism and the rise of peasant nations within the nation Chiapas in r I and d quot 39 r r quot Journal ofPeasant Studies 32 3 4651691 Brosius J P 1997 Endangered forest endangered people Environmentalist representations of indigenous knowledge Human Ecology 25 14769 Hale C R 2002 Does multiculturalism menace Governance cultural rights and the politics of identity in Guatemala Journal of Latin American Studies 34485524 Dove M R 2006 Indigenous people and environmental politics Annual Review of Anthropology 35191208 Greene S 2006 Getting over the Andes The geoecopolitics of indigenous movements in Peru s twentyfirst century Inca empire Journal of Latin American Studies 38327354 Perreault T 2001 Developing identities I J39 39 quot39 quot rural quot quot39 J and resource access in Ecuadorian Amazonia Ecumene 8 43814l3 Silberling L S 2003 Displacement and quilombos in Alcantara Brazil modernity identity and place International Social Science Journal 55 ll45 Week Nine Globalization and the Neoliberalism in Peasant Economies Kay C 2003 Chile s neoliberal Transformation and the peasantry J angrarian Change Vol 2 4 464501 HechtSB Divergent Deforestation Ms Nevin and Peluso In Press Products and processes of Commodi cation in SE Asia Reader Week Ten Futures of Peasantries Kay C 2006 Rural poverty and development strategies in Latin America Journal of Agrarian Change 6 4455508 McMichael P 2006 Reframing development Global peasant movements and the new agrarian question Canadian Journal of Development Studies Revue Canadienne D Etudes Du Developpement 27 447l483 Bebbington A 1999 Capitals and capabilities A framework for analyzing peasant viability rural livelihoods and poverty World Development 27 l2202l2044 Bebbington A J and S P J Batterbury 2001 Transnational livelihoods and landscapes Political ecologies of globalization Ecumene 8 4369380 Bakx K 1990 Shanty town the Final Stage of Rural Development Reader Kearney M 1996 Beyond Peasant Studies Reconceptualizing the Peasantry Bebbington A 2002 Capitals and Capabilities World Development Segregation Indices and their Functional Inputsl Rick Grannis Cornell University and RAND January 23 2002 1 Direct all correspondence to Rick Grannis Department of Sociology Cornell University Ithaca NY 14853 rdg25cornelledu Functional Inputs Segregation Indices and their Functional Inputs Multi Group Indices Reardon and Firebaugh s 2002 advocacy of multigroup segregation indices is an important contribution to the index debate a debate of central importance to understanding segregation Indices guide and circumscribe all comparisons both over time and between cities all correlations with other variables and all classi cations Jahn Schmid and Schrag 1947 More importantly they operationalize segregation theory itself and thus circumscribe all substantive understandings Reardon and Firebaugh s 2002 review of multigroup indices highlights the fact that twogroup indices have guided our thinking about segregation Indices reduce huge data arrays into simpler more readily understandable numbers Regardless of the formula one uses to reduce such arrays the formula itself is merely a function of those arrays and only those arrays Before choosing formulas segregation researchers need to consider how their choice of inputs guides their theoretical development Only when one has correctly determined which variables are appropriately included in the discussion of segregation can one proceed to develop indices and build definitions and theories Reardon and Firebaugh s 2002 formulabased criterion for segregation indices excluded other potentially important multigroup indices They identified siX measures which they evaluated against desirable properties of segregation indices adapted from Functional Inputs Schwartz and Winship s 1980 and James and Taeuber s 1985 original four criteria the principle of transfers compositional invariance size invariance and organizational equivalence These criteria however concern only the racial populations of each neighborhood and thus have no meaning for indices that include other variables In fact all of Reardon and Firebaugh s 2002 multigroup measures can be derived from exactly the same set of data a matrix whose rows consist of neighborhoods whose columns consist of groups and whose cell entries consist of the number of persons of the group represented by the column in the neighborhood represented by the row Multi Dimensional Indices The distinction of considering multigroup segregation instead of dichotomous segregation is profound it involves including new variables in the functions one for each additional racial group or adding new columns to the data matrix being reduced However the decision to include or to exclude other variables such as neighborhood contiguity tract area or proximity to the central city is as fundamental to the understanding of segregation data as is the choice of whether or not to restrict the scenario to a majority race and a single minority race or to allow for a multiplerace scenario This is the issue of multidimensional inputs to segregation indices and it re ects the multidimensional nature of spatial segregation This is a topic that Reardon and Firebaugh 2002 do not address and it is at least as important as their distinction between twogroup and multi group segregation Functional Inputs Below I consider some properties of multigroup segregation indices with multi dimensional inputs I show that indices can best be understood in terms of the variables they are functions of and that accounting for the location of neighborhoods with respect to each other is as important as analyzing multiple racial groups I conclude by proposing a multi group spatial proximity index Indices as Functions In addition to the racial population of each neighborhood what other variables might we consider In addition to Reardon and Firebaugh s 2002 six multigroup indices Massey and Denton s 1988 classic survey of segregation indices identi ed twenty more distinct formulas used to measure aspects of segregation We can reduce these twentysix indices to a set of simple functions and illustrate them in terms of the variables they use as inputs to show how our choice of indices defines segregation and profoundly in uences our understanding of this phenomenonz Table 1 lists the indices3 An Appendix available from the author on request discusses how analyzing functional inputs relates to factor analyses 3 For simplicity s sake I use only the generalized version of the Atkinson index The three versions of it used by Massey and Denton 1988 are easily derivable by substitution I also use only the interaction index and its distancedecay counterpart The isolation index and its distancedecay counterpart are corollaries equaling unity minus the interaction indices Functional Inputs and cites their original appearance in the literature Table 2 displays their computational formulas Tables 1 and 2 about here Table 3 lists the indices as functions of the variables4 they use as inputs Table 3 about here Each index is a function of between two and eleven variables Through inspection alone some patterns are obvious and algebra makes numerous other patterns apparent Table 4 lists the indices as functions of this reduced set of input variables Table 5 categorizes indices by their common input variables and describes their inputs more fully Tables 4 and 5 about here This new list represents those variables and only those variables which a segregation researcher would have to find values for in order to calculate these indicess An Appendix available from the author on request discusses of how I identified these variables and summarizes the algebraic transformations 5 For example one counts the number of minorities in a neighborhood or the number of majority group members in a neighborhood but one does not count a Functional Inputs Some indices dissimilarity Gini entropy Atkinson isolation and the correlation ratio are functions of the minority population and the majority population of each neighborhood and only those variables These indices are more widely used than any other segregation measures and much of the debates about indices refer only to these Most segregation researchers by considering only members of this group have implicitly argued that the only two arrays of numbers the majority population of the neighborhoods and the population of a single minority group of each neighborhood are important for understanding segregation and that no other information is necessary Reardon and Firebaugh s 2002 multigroup indices are extensions of these indices to the multi group case Spatial Proximity Some indices absolute and relative clustering distancedecay isolation and spatial proximity are primarily concerned not with the distribution of the minority and majority populations across neighborhoods but with the distribution of minority and majority neighborhoods with respect to each other White 1983 termed this the checkerboard problemquot If one allows the squares on a checkerboard to represent neighborhoods once the composition of each square is given any spatial rearrangement proportion One calculates a proportion from counted values Similarly the sums of neighborhood populations are just that sums One had to identify neighborhoods and count their populations Functional Inputs of them will result in the same calculation for most segregation indices Thus A city in which all the nonwhite parcels were concentrated into one single ghetto would have the same calculated segregation as a city with dispersed pockets of minority residents White 1983 pp 10101011 These clustering indices can all be rewritten in terms of a single function fXiYj Zi1Zji inin 1 This function focuses on the potential for interactions and is explicitly defined in terms of the product of the number of individuals of the specified groups in the set of neighborhoods defined by the contiguity matrix C All of these indices can be thought of as interaction measures except that instead of assuming the potential for interaction exists only among residents of a single neighborhood eg census tract they assume the potential for interaction exists between residents of neighborhood i and all other neighborhoods defined as contiguous to i by the contiguity matrix C C could also be defined as a weight such as inverse distance so that neighborhoods that were closer were weighted more heaVily while neighborhoods that were further away were weighted less heaVily The formulas for the clustering indices then translate into Distancedecay Isolation fxiXyj ftjl 2 Absolute Clustering fXiXj fX2n392 fXitj fX2n39z 3 Functional Inputs Relative Clustering Y2 fxixJ X2 fyiyj 7 l 4 Spatial Proximity fXiXjX fYiYjY faiatij 5 The distancedecay isolation index can be interpreted as the probability that the next person a group X member meets is from group Y The absolute clustering index measures how much group x members are clustered so that they interact with each other more than one would expect as a proportion of how much opportunity group x members have to interact with anyone more than one would expect The relative clustering index compares the average proximity of members of group X to the average proximity of members of group Y The spatial proximity index is the average of intragroup proximities weighted by each group s fraction in the population In short the distance between groups or the geographic level at which they are segregated as well as the fact that they are separated has been a concern of previous research It would be useful to combine Reardon and Firebaugh s 2002 focus on multiple groups with this concern for the dimension of distance An Example While segregation researchers are certainly aware of the presence and importance of ghettos and the spatial patterning of neighborhoods there is a tendency to revert to more simplistic measures when analyzing more complex relationships I illustrate one such complexity by reexamining some data from an article by Farley et al 1994 that Functional Inputs began by examining residential segregation scores using the dissimilarity index for metropolitan Detroit in 1990 controlling separately for household income and for educational attainment Since they used only the dissimilarity index Farley et al l994 s analysis utilized only two arrays of numbers to compute their index scores for each subset Using the same data as Farley et al 1994 I computed the dissimilarity index to replicate their results the isolation index and the spatial proximity index for each of their income and educational subsets The isolation index is perhaps the second most commonly cited index and like the dissimilarity index uses only information about the number of white and black households in the tract Computing the spatial proximity index required using one additional array of numbers which tracts in the Detroit metropolitan area were contiguous and which were not Figures 1 and 2 display the results Figures 1 and 2 about here In both gures the line represented by long dashes and triangles represents the dissimilarity index scores the line with short dashes and circles represents the isolation index and the solid line with squares represents the spatial proximity index As Farley et al 1994 noted the dissimilarity index is essentially unaffected by changes in income The isolation index behaves similarly Using one or both of these indices which only use information about the numbers of white and black households in each tract one might reasonably conclude that segregation is unaffected by changes in income Functional Inputs or educational attainment as did Farley et al 1994 Segregation as measured by the spatial proximity index however drops dramatically with increases in income or educational attainment Thus two ndings emerge from these gures First in Detroit blacks with high incomes and high education are just as likely to be segregated at the tract level as blacks with low incomes and little education as shown by the dissimilarity or isolation indices Second however the tracts that blacks with high incomes and high education live in are much more likely to be adjacent to white tracts than are the tracts occupied by blacks with low incomes and little education While income and education do not allow blacks in Detroit easy access into white tracts they do allow them access into tracts in larger white areas Segregated neighborhoods of 1300 households the average tract size in this region may be suf ciently large to segregate most facetoface interactions but may not be suf ciently large to segregate supermarkets school districts or churches Upperclass blacks live in smaller mostlyblack communities than do their less welltodo counterparts Using indices that only account for the distribution of whites and blacks at the tract level misses this second important and powerful nding Multi Group Spatial Proximity While Reardon and Firebaugh 2002 use organizational units instead of neighborhoods to maximize generality ie with school districts etc this simpli cation ignores important differences between neighborhoods and schools not the least of which Functional Inputs is that school districts are often much bigger than the neighborhood equivalents we typically measure residential segregation by e g a high school feeder zone may include several census tracts and numerous census block group Much of the theorizing done about residential segregation would not have any meaning at the microlevel at which Reardon and Firebaugh s 2002 indices as well as many traditional segregation indices would measure it concerning only very small communities of a few hundred or a thousand households oblivious to larger patterns This has not been a critical issue in the past since segregation has primarily been measured in a twogroup scenario black and white Given the ghettoization of blacks throughout America segregation at the neighborhood level typically implied larger scale segregation Massey and Denton 1993 As we begin to consider more complex multigroup cases however the disparity between microlevel segregation and larger patterns may become more acute It is appropriate that as we begin to consider more widespread use of multigroup measures we simultaneously consider using spatial proximity measures more The spatial proximity index has an obvious adaptation to the multigroup case MultiGroup Spatial Proximity 2m fXimijXm REEDT 6 2m Xiijmcij titjcijT This new index is the average of intra group proximities weighted by each group s fraction in the population The numerator is the sum of several terms one for Functional Inputs each racial group Each term is the total number of potential interactions among members of each racial averaged over the number of members of that racial group The denominator equals the total number of potential interactions between all individuals averaged over the total number of people in the study area Since this index is a sum of an independent term for each racial group this index could be used effectively to measure spatial proximity among a single racial group two racial groups or several It could also be expanded to measure spatial proximity among different subcategories e g income educational level etc within a single racial group or among multiple racial groups Researchers need to consider indices that account for nearby neighborhoods unless they are certain the boundaries of census tracts block groups or other neighborhood proxies completely con ne the experience of segregation Using clustering indices such as the multigroup spatial proximity index proposed above also allows one to deal with the Modi able Areal Unit Problem MAUP MAUP results from the imposition of arti cial boundaries on a geographically correlated phenomenon Openshaw and Taylor 1979 Analytical results may be highly sensitive to the size and boundaries of the zones used Dramatically different results may be obtained from the same set of data when the information is grouped in different levels of spatial resolution scale effect or by merely altering the boundaries or con gurations of the zones at a given scale of analysis zone effect Using the smallest possible neighborhood equivalent in combination with a clustering index would allow one to account for Functional Inputs segregation patterns at or above the level of analysis While the availability of data limits our analyses we should not allow our analytic tools to be more limiting than our data Conclusion In choosing the indices by which they measure segregation sociologists de ne segregation itself and induce particular substantive understandings When we use indices we are trying to reduce huge data arrays into simpler more readily understandable numbers While no index will be useful for every study of segregation due to the importance of measuring both neighborhoodlevel and largerlevel segregation patterns indices that include distance or contiguity as an input should be used more often in future segregation research Furthermore the definition of contiguity or distance as used in these measures needs to remain adaptable to account not only for geographic distance or adjacency but also for the actual probabilities of contact6 When researchers choose to ignore information about the racial composition of nearby neighborhoods they are making assertive theoretical claims that segregation only For example Grannis 1998 has argued that in addition to mere geographic contiguity it is important to note whether residential streets connect neighborhoods to each other Therefore one could let the contiguity or distance variables in these indices refer to residential street connectivity or distance or any other appropriate measure of the actual potential for interaction Functional Inputs occurs at or below the level of the neighborhood they are using e g census tract and that life in a minority community of a few hundred or a thousand households in the midst of a majority population is not conceptually different from life in a minority community of a hundred thousand households since they fail to incorporate data which would allow them to distinguish these two situations Just as multigroup segregation indices are important for understanding complex demographic patterns so indices that include data on neighborhood contiguity are important for understanding segregation patterns occurring at levels larger than a census tract Functional Inputs References Atkinson A B 1970 On the Measurement of Inequality American Sociological Review 43865880 Bell Wendell 1954 A Probability Model for the Measurement of Ecological Segregation Social Forces 32 357364 Carlson Susan M 1992 Trends in racesex occupational inequality Conceptual and measurement issues Social Problems 39269290 Dacey Michael F 1968 A Review on Measures of Contiguity for Two and KColor Maps Pps 479495 in Spatial Analysis A Reader in Statistical Geography Brian J L Berry and Duane F Marble editors PrenticeHall Duncan Otis D and Beverly Duncan 1955 quotA Methodological Analysis of Segregation Indices American Sociological Review 20210217 Duncan Otis D Ray P Cuzzort and Beverly Duncan 1961 Statistical Geography Problems in Analyzing Area Data Free Press Farley Reynolds Charlotte Steeh Maria Krysan Tara Jackson and Keith Reeves 1994 Stereotypes and Segregation Neighborhoods in the Detroit Area American Journal ofSociology 100750780 Geary R C 1954 The Contiguity Ratio and Statistical Mapping Incorporated Statistician 5 1 15 141 Goodman Leo and William H Kruskal 1954 Measures of association for cross classi cations Journal ofthe American Statistical Association 49 731764 Functional Inputs Grannis Rick 1998 The Importance of Trivial Streets Residential Streets and Residential Segregation American Journal ofSociology 103 15301564 Hoover Edgar M 1941 Interstate Redistribution of Population 18501940 Journal ofEconomic History 1199205 Jahn Julius A Calvin F Schmid and Clarence Schrag 1947 The Measurement of Ecological Segregation American Sociological Review 103 293303 James David R and Karl E Taeuber 1985 Measures of Segregation Pp 132 in Sociological Methodology 1985 edited by Nancy Tuma JosseyBass James Franklin J 1986 A new generalized exposurebased segregation index Sociological Methods andResearch 14301316 Lieberson Stanley 1981 quotAn Asymmetrical Approach to Segregationquot Pp 6182 in Ethnic Segregation in Cities edited by Ceri Peach Vaughn Robinson and Susan Smith Croom Helm Massey Douglas S and Nancy A Denton 1988 The Dimensions of Residential Segregation Social Forces 67 281305 Morgan Barrie S 1975 The segregation of socioeconomic groups in urban areas A comparative analysis Urban Studies 124760 7 1983 quotAn Alternate Approach to the Development of a DistanceBased Measures of Racial Segregationquot American Journal ofSociology 88 12371249 Openshaw S and P Taylor 1979 A Million or so Correlation Coefficients Three Experiments on the Modi able Area Unit Problem Pp 127144 in Statistical Applications in the Spatial Sciences edited by Neil Wrigley London Pion Functional Inputs Reardon Sean F and Glenn Firebaugh 2002 Measures of MultiGroup Segregation Sociological Methodology Sakoda J 1981 A generalized index of dissimilarity Demography 18245250 Schwartz J and C Winship 1980 The Welfare Approach to Measuring Inequality Pp 136 in SocialMethoals edited by Schessler Jossey Bass Theil Henri 1972 Statistical Decomposition Analysis NorthHolland Theil Henri and Anthony J Finezza 1971 A note on the measurement of racial integration of schools by means of informational concepts Journal of Mathematical Sociology 1 1 87 194 White Michael J 1983 39The Measurement of Spatial Segregation American Journal ofSociology 98 10081019 7 1986 39Segregation and Diversity Measures in Population Distribution Population Index 52 2 198221 Functional Inputs Table 1 Original Citation of Segregation Indices Segregation Index Citation Absolute Centralization Massey and Denton 1988 Absolute Clustering Massey and Denton 1988 adapted from Geary 1954 and Dacey 1968 Absolute Concentration Massey and Denton 1988 Atkinson Atkinson 1970 Correlation Ratio Bell 1954 White 1986 Delta Duncan Cuzzort and Duncan 1961 adapted from Hoover 1941 Dissimilarity Duncan and Duncan 1955 Distancedecay Isolation Morgan 1983 Entropy Theil and Finizza 1971 Theil 1972 Gini Duncan and Duncan 1955 Isolation Bell 1954 Lieberson 1981 Multigroup Dissimilarity Morgan 1975 Sakoda 1981 Multi group Gini Reardon and Firebaugh 2002 Multi group Information Theil and Finezza 1971 Theil 1972 Multi group Normalized Exposure Multigroup Relative Diversity James 1986 Goodman and Kruskal 1954 Carlson 1992 Multigroup Squared Coefficient of Variation Reardon and Firebaugh 2002 Proportion in Central City Massey and Denton 1988 Relative Centralization Duncan and Duncan 1955 Relative Clustering Massey and Denton 1988 Relative Concentration Massey and Denton 1988 Spatial Proximity White 1986 Functional Inputs Table 2 Computational Formulas for Segregation Indices Segregation Index Formula Absolute Centralization Absolute Clustering Absolute Concentration Atkinson Z Xi1Ai39 Z XiAiil 2 Xigt02 Cinjl Xnzzz cit1 ZXiXZciitil Xnzzz can 1 2 XiaiX ani1tiaiT1 mm miT2 2 tiaiT1 1 Pl PlZ 1 pi 139kgtpiktiPTI M Correlation Ratio xPx P1 P Where xPx Z XiXHXiti Delta 12 Z lXiX aiAl Dissimilarity Z tilpi PlZTPU P Distancedecay Isolation Z XiX Z Kijyjtj where Kii CiitiZ Ciiti Entropy Z tiE EiET where E Plog1P 1 Plog11 P Ei Pi10g1 Pi t 1 pi10g11 PD Gini 22 titilpi pil2T2P1 P Isolation Z XiXHXiIi Multigroup Dissimilarity Multigroup Gini Multigroup Information Multigroup Normalized Exposure Multigroup Relative Diversity Multigroup Squared Coef cient of Variation 12TI 22 ti nimnml 12TZI 222 mi mmmml 1TE 22 ti mm MumWm UT 22 ti mmWm2 lnm 1TI 22 ti mmMY 1TM1 22 tj mmmu2 Wm Proportion in Central City chX Relative Centralization Relative Clustering Relative Concentration Spatial Proximity 2 Xi1Y139Z XiYil PxxPyy 7 l where Pxx ZZ XincijXz Pw ZZ iniciiYz 2 XiaiDiHZ yiaiYl 1 ZMH tiaiT1Z inzmiTn 1 XPxx YPyyTPn where Pu titjcijTZ Pxx 22 XinCijX2 Pw ZZ iniciiYz Functional Inputs Table 2c0ntinued Notation 61 equals each neighborhood 1 393 land area A equals the urban region s land area 01 is a dichotomous variable that equals one when neighborhoods i and j are contiguous and zero otherwise E Zm1Mnm1nm I 2m1M nm lnl11m M the number of groups being considered 71 equals the number of neighborhoods 1 in the urban area p equals neighborhood 1 s minority proportion P equals the urban region s minority proportion t equals neighborhood 1 s total population T equals the urban region s total population x equals each neighborhood 1 39s minority population X equals the urban region s minority population X W equals the number of minorities living within the boundaries of the central city y equals each neighborhood 1 39s majority group population Y equals the urban region s majority population 713m equals the proportion in group m Irm equals the proportion in group In of those in unit j When the Neighborhoods are Ordered by Land Area from smallest t0 largest 111 equals the rank of the neighborhood where the cumulative population of neighborhoods equals X the study area s minority population summing from the smallest neighborhood up 112 equals the rank of the neighborhood where the cumulative population of neighborhoods equals Y the study area s majority group population summing from the largest neighborhood down T1 equals the cumulative population of neighborhoods one to 111 T2 equals the cumulative population of neighborhoods 112 to 71 When the Neighborhoods are Ordered by increasing Distance from the Central Business District A equals the cumulative proportion of land area through neighborhood 1 X equals the cumulative proportion of minorities through neighborhood 1 Y equals the cumulative proportion of maj ority group members through neighborhood 1 7 Massey and Denton 1988 used eXpdj or the negative exponential of the distance between the centroids of i and j to estimate contiguity Table 3 Functional Inputs Input Variables for Segregation Indices Segregation Index Input Variables Constants Vectors Matrices Orderings Absolute Centralization a X 02 Absolute Clustering n X t X C Absolute Concentration n1 n2 T1 T2 a t X 01 Atkinson P T p t Correlation Ratio P X t X Delta A X a X Dissimilarity P T p t Distancedecay Isolation X t X y C Entropy P T p t Gini P T p t Isolation X t X Multigroup Dissimilarity T I t 11 Multigroup Gini T I t 11 Multigroup Information T E t 11 Multigroup Normalized T T 11 Mosure Multigroup Relative T I T 11 Diversity Multigroup Squared M T t 11 Coef cient of Variation Proportion in Central City X ch Relative Centralization X y 02 Relative Clustering X Y X y C Relative Concentration n1 n2 T1 T2 a t X y 01 X Y Spatial PrOXimity T X Y t X y C Functional Inputs Table 3c0ntinued Notation ail cci ti nim Xi yi Cu see Table 1 see Table l the ordering of the neighborhoods by land area from smallest to largest the ordering of the neighborhoods by increasing distance from the central business district 717m Table 4 Functional Inputs Reduced Set of Input Variables for Segregation Indices Segregation Index Input Variables Vectors Matrices Orderings Absolute Centralization a X 02 Absolute Clustering X y C Absolute Concentration a X y Atkinson X y Correlation Ratio X y Delta a X Dissimilarity X y Distancedecay Isolation X y C Entropy X y Gini X y Isolation X y Multigroup Dissimilarity t1 t2 Multigroup Gini t1 t2 Multigroup Information t1 t2 Multigroup Normalized EXposure t1 t2 Multigroup Relative Diversity t1 t2 Multigroup Squared Coef cient of Variation t1 t2 Proportion in Central City cc X Relative Centralization X y 02 Relative Clustering X y C Relative Concentration a X y Spatial PrOXimity X y C Table 5 Functional Inputs Segregation Indices Grouped by Shared Variables Input Variables Minority and Majority populations of individual neighborhooods X y Indices Atkinson Correlation Ratio Dissimilarity Entropy Gini Isolation Racial populations of individual neighborhoods t1 t2 Minority and Majority populations of individual neighborhoods and Neighborhood Contiguity C x y Multigroup Dissimilarity Multi group Gini Multi group Information Multigroup Squared Coefficient of Variation Multigroup Relative Diversit Multigroup Normalized EXposure Absolute Clustering Distancedecay Isolation Relative Clustering Spatial Proximity Minority and Majority populations and land Area of individual neighborhoods a X y Absolute Concentration Relative Concentration Minority population and land Area of individual neighborhoods a X Minority population and land Area of individual neighborhoods and neighborhood Ordinal Distance from Central business district a 02 X Minority and majority populations of individual neighborhoods and neighborhood Ordinal Distance from Central business district X 02 y Minority population of neighborhood and whether neighborhood is in central city cc X Delta Absolute Centralization Relative Centralization Proportion in the Central City Functional Inputs Figure 1 Black white Segregation in Detroit metropolitan area by Income quot39 o a a quot i f Lessthan 5000to 10000 15000 25000 35000 50000 75000 100000 5000 9999 to to to to to to 14999 24999 34999 49999 74999 99999 0139 more Dissimilarity O Isolation Spatia1 Proximity
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'