Reason, Passion, & Cognition, Week 1 Notes
Reason, Passion, & Cognition, Week 1 Notes 88-120
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This 5 page Class Notes was uploaded by Monica Chang on Sunday September 4, 2016. The Class Notes belongs to 88-120 at Carnegie Mellon University taught by Julie Downs in Fall 2016. Since its upload, it has received 86 views. For similar materials see Reason, Passion, and Cognition in Social & Decision Sciences at Carnegie Mellon University.
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Date Created: 09/04/16
Week 1 INTUITIVE PSYCHOLOGY IN PROBABILITY AND RANDOMNESS Probabilistic reasoning - The Monty Hall Problem is an example of how bad our intuitions are when talking about single probabilities, not to mention combining probabilities - Base rate neglect (we pay too much attention to diagnostic info, and forget base rates) o Compound probabilities Example 1: Disease with 1/1000 prevalence, a false positive rate of 5%, correctly diagnoses those w/ the disease. What is the probability that those tested to be positive have the disease? Intuitive answer: 95% Correct answer: ~2% Explanation: Example 2: Linda problem, stereotyping Frequency vs. probability - Higher frequency does not mean higher probability o Example 1: You get a reward if you get a red ball. You have two options: 1) draw from a small urn with 1 red ball and 9 black balls or 2) draw from a big urn with 9 red balls and 91 black balls. Which option do you choose? Intuitive answer: Draw from big urn Correct answer: Draw from the small Explanation: Draw from the small urn because you have a 10 % chance of drawing a red while the big urn only gives you a 9% chance. Most people still choose the big urn because their intuition tells them to choose from the one with a greater frequency of reds. Probability matching - Probability matching is intuitive but mislead o Example 1: Guess the next color. For every correct answer, you get $1. The chances of the color being blue is 70% and the chances it’s yellow is 30%. What strategy did you use to guess the color? Intuitive answer: Guess blue 70% of the time and yellow 30% of the time. Correct answer: Guess blue 100% of the time. Explanation: You have a greater chance of getting blue each time. 0.7*0.7 + 0.3*0.3 = 0.58 intuitive probability matching 0.7*1.0 + 0.3*0 = 0.70 guessing blue 100% of the time 0.70 > 0.58 therefore, 2 nd strategy is better o Example 2: Predicting basketball finals Streaks and runs - Negative Recency Bias: when a sequence of events seems random, people intuitively want to predict the next event to be the opposite from the one before o Example 1: A coin lands on tails 4 times in a row. Predict what side will be more likely on the next flip. Intuitive answer: The next one will more likely be heads. Correct answer: The next one will have basically an equal chance of being heads or tails. Explanation: Each event/flip is independent so assuming the coin is fair, it should be equally likely to land on either side. There is a misconception that fairness applies to small samples, but we have to remember that there is randomness, so as the Law of Large Numbers states, with enough trials, the outcome percentages should match the probabilities. In other words, if you were to flip a coin 100 times, you’d expect close to 50 heads and 50 tails, but if flipping a coin 10 times didn’t give you close to 5 heads and 5 tails, you wouldn’t be as surprised. o Example 2: Gamblers Fallacy (Monte Carlo Fallacy), Casinos o Example 3: When a mother has 8 girls, and is told her chances of getting a boy as a ninth child is much greater is a misconception - Positive Recency Bias: when a sequence of events doesn’t seem random, people intuitively want to predict the next event to have the same outcome as the one before not random o Hot hand Example 1: Basketball player’s shots. There’s a misconception that numbers of successive hits should exceed number produced by chance (but of course basketball skill is another factor). In a Cornell basketball experiment, they found the players’ 50% accuracy distance and had the players shoot 100 baskets from there. Out of the 100 shots: P(H|H) = 45.6% P(H|M) = 51.2% Number of runs (HH+) = 46.3 Expected number of runs (HH+) = 47.3 Regression to the mean - Regression to the Mean is a phenomenon where high or low outcomes are more likely to go towards the average outcomes the next time around o Example 1: Air Force Pilot claims that praise is better than punishment because when he praised his students they tended to do worse, and when he criticized them, they tended to do better. He expected the opposite to happen but it makes sense this way because as Daniel Kahneman pointed out, the students that have done well before are more likely to do worse (especially since their skills are limited) and vise versa. o Example 2: If you roll two dice twelve times and get at least a sum of 10 four times, you are less likely to roll a sum of at least 10 for the next twelve times you roll the dice - But there’s skill involved! Performance = skill + luck (or as Daniel Kahneman stated success = talent + luck) o Example 1: If you are a very tall parent, your children are more likely to be shorter and vise versa. Height = genetic factors + random factors o Others examples: many placebo effects, Sports Illustrated “jinx”, actions taken to stop a wave of crime will work, etc. Key ideas - Our intuitions can be incorrect and misleading, but we often follow them anyway - Key concepts include: o Base rate neglect o Probability matching o Negative recency bias (e.g. Gambler’s Fallacy) o Positive recency bias o Regression to the mean - Faulty reasoning and naïve theories often lead us to make wrong inferences from data and wrong predictions - Looking ahead: So how should we make decisions? NOTES on Plous, S. (1993). The Psychology of Judgment and Decision Making. Chapter 14 – The Perception of Randomness, pp. 153-161. Perceiving Randomness: - Coincidences happen more often than we think is likely - The probability an event happening is much more than the probability of a specific instance of that event (e.g. Some person having the same birthday as some friend is more likely than your friend having the same birthday as you). - People will often believe there are patterns in random series of stimuli. Refer to Christopher Peterson’s study in 1980 for an example. People often let their own behavior in the past influence their predictions in the future when in fact, the future events are independent of their past behavior (even in instances when they know events are random). - We are often biased in thinking that alternating patterns between two outcomes are more random than streaks of the same outcome. Refer to Willem Wagenaar’s study in 1970 for an example. Evidence also shows that when you increase the number of outcomes, people will be more likely to view a repeated outcome as nonrandom. In general people expect sequences to vary more than they would if they were truly due to chance. - Evidence shows however, that incorrect perceptions of randomness and be corrected with training. Refer to Allen Neuringer’s study in 1986 for an example. Big Ideas: - In the real world, people and professionals often over-analyze chance events and think things are predictable (e.g. the stock market, sports, etc.) - If independent events are equally likely, we should be careful not to interpret repeated occurrences of one outcome as meaningful. However, if certain events have a lower probability, repeated occurrences may give insight into something more.
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