The device acts as a pop-up barrier to prevent the passage of a vehicle. It consists of a 100-kg steel plate AC and a 200-kg counterweight solid concrete block located as shown. Determine the moment of inertia of the plate and block about the hinged axis through A. Neglect the mass of the supporting arms AB. Also, determine the initial angular acceleration of the assembly when it is released from rest at u = 45.
Reasoning and decision making REASONING & DECISION MAKING Formal Logic & Reasoning ● Normative (or prescriptive): how people ought to reason ○ Optimal or correct (e.g. logical) reasoning and rational choice ● Descriptive reasoning: how people actually reason ○ We sometime ignore relevant information, or err in other ways ○ e.g. be persuaded by information that isn’t relevant ○ e.g. show various types of bias ○ Conjunction fallacy: the probability of two outcomes combined is more likely than one of the outcomes separately (“Linda is a bank teller and a feminist activist” is more likely than “Linda is a bank teller”) Logical reasoning ● Inductive: probabilistic inference based on experience ○ i.e. reach (infer) a likely conclusion based on specific facts or observations ○ e.g. all US presidents have been white so the next president will be white (this seems to be a reasonable inference but it was wrong) ● Deductive reasoning: drawing certain conclusions from assumed (given) premises ○ e.g. we know our friend has a swan and we’ve never met it but we assume it’s white ○ e.g. if it is raining, then there are clouds. It is raining. (conclusion: there are clouds) ○ Syllogism: two or more assertions (premises) lead to a conclusion ● Validity: conclusion follows from premises (form) ● Truth: conclusion is true (content) ● Soundness: validity + truth ● It is possible to have a valid argument and a false conclusion or vice versa ● Validity and truth are independent of each other in principle but these things get a little mixed up in people’s minds ○ People are more likely to think the whole argument is valid if they believe the conclusion ● The BeliefBias Effect: we tend to see arguments with true conclusions as valid and arguments with false conclusions as invalid ○ People are more likely to think the whole argument is valid if they believe the conclusion ○ People are less likely to think the argument is valid if they don’t believe the conclusion Limitations and Common Errors of Deduction ● Belief bias effect ● Inherent limitation: only concerned with validity, not truth ○ If the premises are true, then it’s true ● Confirmation (positive) bias: when generating possible solutions, we should seek falsification but often seek positive answers ○ We look for things that support validity ○ Watson Selection Task: got people to do a selection task that could be solved perfectly with deduction ■ There were cards with letters on one side and numbers on the other ■ He would give them rules and ask if the cards fit the rules ■ Why are concrete problems so much easier (such as drinking age questions rather than card questions) ● Logical (formal) fallacies: failures to follow rules of logic by drawing conclusions that: ○ Affirm the consequent ■ e.g. if the design is flawless, the space shuttle will work. The space shuttle works. Therefore, the design is flawless Deny the antecedent ■ e.g. if my paper is flawless, then I’ll get an A. My paper is not flawless. Therefore, I won’t get an A. Thinking and DecisionMaking under natural or uncertain conditions ● Thinking often appears to be irrational and inconsistent ● We often use judgement heuristics, or strategies that are easy to apply, often lead to reasonable decisions, but may lead to poor decisions ● Thinking that appears to be irrational or inconsistent may reflect adaptive limitations (e.g. for speed or efficiency) Theories of Decision Making ● Common but naive assumption: we make decisions to maximize the expected value ○ Value reflects both objective gains/losses and probability of occurrence ● Expected value: objective usefulness or value that will determine decisions ○ e.g. people will select the option that has the highest monetary value ○ This is a normative and frequently violated theory ● Expected Utility Theory: (subjective) usefulness or personal value, not objective value, guides decisions ○ Ten dollars doesn’t mean the same to everyone else, so we have to take the subjective usefulness of things into account ○ This is better, but people are inconsistent regarding both objective value and subjective utility ● Prospect Theory: differs from expected utility theory in several ways ○ Doesn’t rely on utility or value because it takes into account the various biases people have ○ Consequences are viewed in terms of changes from a reference level (usually current state, like a sensory adaptation level) with a diminishing returns function for both positive and negative outcomes ■ Once you’ve got some money, it loses value to you ■ e.g. $1 vs. $11 doesn’t seem as different as $1000 vs. $1011 because your reference level has changed ■ Moving a milk jug will seem a lot lighter after moving cinder blocks rather than empty water bottles ○ We don’t weigh outcomes in an objective way ■ People tend to overweight unlikely events (mega lottery) and they tend to underweight things that are very likely ○ Value function is steeper for losses than gains (this implies loss aversion) ■ e.g. losing $100 hurts more than gaining $100 pleases ■ Empirical results indicate losses are about 2x as painful as gains are pleasurable ■ Loss aversion: value function is steeper for losses than gains