Representativeness Heuristic and Conjunction Errors. Risk Attitude and Framing Effects

Transcription

1 1st: Representativeness Heuristic and Conjunction Errors 2nd: Risk Attitude and Framing Effects Psychology 355: Cognitive Psychology Instructor: John Miyamoto 05/30/2018: Lecture 10-3 Note: This Powerpoint presentation may contain macros that I wrote to help me create the slides. The macros aren t needed to view the slides. You can disable or delete the macros without any change to the presentation.

2 Psych 355, Miyamoto, Spr '18 Definition of the Representativeness Heuristic 2 Outline The Representativeness Heuristic Conjunction errors - one consequence of people's use of the representativeness heuristic. Risk attitude Framing effects - the Asian Disease Problem

3 Representativeness Heuristic Event A is more representative than Event B Event A is more probable than Event B "more representative" means "more similar to a stereotype of a class or to a typical member of a class." Representativeness Heuristic: Judge the probability of an event E by the representativeness of the event E. Psych 355, Miyamoto, Spr '18 Why Does the Representativeness Heuristic Cause Reasoning Errors? 3

4 Representativeness Heuristic (cont.) Event A is more representative than Event B Event A is more probable than Event B Representativeness Heuristic: Judge the probability of an event E by the representativeness of the event E. Why does this cause reasoning errors? People make reasoning errors when they focus only on similarity, and overlook other factors that are also relevant to the probability of an event. Example: Base rate neglect as demonstrated in the lawyer/engineer problem. o People focus on the similarity of the description of Jack to the stereotypes of a lawyer and of an engineer. They fail to take into account the base rate of lawyers and engineers (30/70 or 70/30). Psych 355, Miyamoto, Spr '18 Conjunction Fallacies - The Linda Problem 4

5 Conjunction Fallacies The Famous Linda Problem Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. F: Judge the probability that Linda is a feminist. T: Judge the probability that Linda is a bank teller. F & T: Judge the probability that Linda is a feminist and a bank teller. Probability Theory: P(F) P(F & T), P(T) P(F & T) Typical Judgment: P(F) > P(F & T) > P(T) This is the typical pattern of a conjunction fallacy. Why Are Conjunction Fallacies Psychologically Interesting? Psych 355, Miyamoto, Spr '18 5

6 Why Conjunction Fallacies Are Psychologically Interesting? 1. Conjunction fallacies strongly support the claim: Human reasoning with uncertainty violates principles of probability theory. 2. Conjunction fallacies also support the claim that people make conjunction errors because they use the representativeness heuristic to judge the probabilities of propositions, F, T and F&T. (Need to provide evidence for these two claims in the following slides) Two Question Regarding Conjunction Fallacies: What is wrong with the judgment pattern: P(F) > P(F & T) > P(T)? How does use of the representativeness heuristic cause people to make conjunction errors? Psych 355, Miyamoto, Spr '18 Probability & the Set Inclusion Principle 6

7 Probability and the Set Inclusion Principle If set B is a subset of set A, then the probability of B must be equal or less than the probability of A. B A P(B) < P(A) Sample Space (set of all possibilities) A B Rationale: When B occurs, A also occurs, so the probability of B cannot exceed the probability of A. Psych 355, Miyamoto, Spr '18 Interpretation of Linda Problem in terms of Set Inclusion 7

8 Conjunction Fallacy Linda Problem: Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Sample Space F F & T T F & T: F: Judge the probability that Linda is a feminist. T: Judge the probability that Linda is a bank teller. Judge the probability that Linda is a feminist and a bank teller. Probability Theory: P(F) P(F & T), P(T) P(F & T) Typical Judgment: P(F) > P(F & T) > P(T) Conjunction Fallacy Psych 355, Miyamoto, Spr '18 Same Slide - No Annotation 8

9 Conjunction Fallacy Linda Problem: Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Sample Space F F & T T F & T: F: Judge the probability that Linda is a feminist. T: Judge the probability that Linda is a bank teller. Judge the probability that Linda is a feminist and a bank teller. Probability Theory: P(F) P(F & T), P(T) P(F & T) Typical Judgment: P(F) > P(F & T) > P(T) Psych 355, Miyamoto, Spr '18 Why Do People Make Conjunction Errors? 9

10 Why Do People Make Conjunction Errors? Remember: The representativeness heuristic predicts that people judge the probability based on how similar the individual case is to a typical member (stereotype) of a group. The description of Linda sounds more similar to someone who is a feminist and a bank teller, than to someone who is only a bank teller. Description of Linda Bank Teller Prototype Feminist Bank Teller Prototype Representativeness Heuristic: People judge probability based on similarity to typical case; they overlook role of set inclusion. Psych 355, Miyamoto, Spr '18 Criticisms of the Representativeness Explanation of Conjunction Fallacies 10

11 Criticisms of This Interpretation Criticism: The Linda problem is just one problem. Reply: Same pattern is found with many similar problems. Criticism: Maybe people think bank teller means someone who is a bank teller and not a feminist. Criticism: Conjunction errors can be eliminated by stating the question in terms of frequencies instead of probabilities. Psych 355, Miyamoto, Spr '18 Summary re Representativeness Heuristic 11

12 Summary re Representativeness Heuristic There is nothing wrong with using similarity as a factor in judging a probability. The problem is that attention to similarity causes people to ignore other factors, like base rates, regression effects and set inclusion, that are also relevant to judging probability. Consequences of the Use of the Representativeness Heuristic Base rate neglect - overlooking relevance of base rate to prediction of outcomes. Conjunction errors - overlooking relevance of set relations to judgments of probabiltiy. Overlooking the importance of sample size to reliability of statistics. Overlooking regression effects in predictions of outcomes. Psych 355, Miyamoto, Spr '18 Two Major Issues in the Psych of Decision Making - Probability & Value 12

13 Two Major Issues in Psychology of Decision Making Judgments of likelihood What outcomes are likely? Which are unlikely? How likely? Slightly possible? Almost certain? Etc. We ve been talking briefly about this topic. Judgments of preference & making choices How strongly do you like or dislike different possible outcomes? How risky are different choices? What risks are worth taking? When should you avoid a risk? Next topic. Psych 355, Miyamoto, Spr '18 Digression re Risk Attitude 13

14 Risk Attitude Risk Aversion: A choice is risk averse if a person chooses a sure-thing X over a gamble G where X is less than the expected value of G. Example of a Risk Averse Decision Prefer a sure win of $500 over a gamble for $1,010 or $0. (Note: Expected value of gamble = $505) Risk Seeking: A choice is risk seeking if a person chooses a gamble G over a sure thing X where the expected value of G is less than X. Example of a Risk Seeking Decision Prefer a gamble for $1000 or $0 over a sure win of $505. (Note: Expected value of gamble = +$500) Same Slide With All Content Displayed Psych 355, Miyamoto, Spr '18 14

15 Risk Attitude Risk Aversion: A choice is risk averse if a person chooses a sure-thing X over a gamble G where X is less than the expected value of G. Example of a Risk Averse Decision Prefer a sure win of $500 over a gamble for $1,010 or $0. (Note: Expected value of gamble = $505) Risk Seeking: A choice is risk seeking if a person chooses a gamble G over a sure thing X where the expected value of G is less than X. Example of a Risk Seeking Decision Prefer a gamble for $1000 or $0 over a sure win of $505. (Note: Expected value of gamble = +$500) Examples of Risk Aversion & Risk Seeking Psych 355, Miyamoto, Spr '18 15

16 Examples of Risk Aversion & Risk Seeking Whenever you buy insurance, you are acting in a risk averse way. The cost of car insurance is a sure loss that is a bigger loss than the expected value of the gamble of driving an uninsured car. Whenever you gamble at a professional casino or in state lottery, you are acting in a risk seeking way. The cost of the lottery ticket is greater than the expected value of the lottery ticket. In a casino, all of the mechanical gambles (roulette or slot machine) have a negative expected gamble. Psych 355, Miyamoto, Spr '18 Is It More Rational to be Risk Averse or Risk Seeking? 16

17 Is It More Rational to be Risk Averse or Risk Seeking? There is no rational requirement to be risk averse. It is equally rational to be generally risk averse or generally risk seeking. It is also rational to be risk seeking for some money quantities, e.g., small amounts of money, and risk averse for other money quantities, e.g., large amounts of money. It is also rational to be risk averse in some domains, e.g., gambles for the health of your children, and risk seeking in other domains, e.g., gambles for business profit and loss. Before the work of Kahneman & Tversky, many theorists thought that people were generally risk averse. Next slide: Reflection effect shows that people are risk averse for some kinds of gambles, and risk seeking for other types of gambles. Psych 355, Miyamoto, Spr '18 Reflection Effect Example 17

18 Reflection Effect Example Choice 1: Which would you prefer? Option A:.80 chance to win $4,000;.20 chance to win $0 Option B: 1.0 chance to win $3,000. Typical preference when gambling for gains Choice 2: Which would you prefer? Option C:.80 chance to lose $4,000;.20 chance to lose $0 Option D: 1.0 chance to lose $3,000. Typical preference when gambling for losses People are typically risk averse for gains and risk seeking for losses. This pattern is called the reflection effect. Psych 355, Miyamoto, Spr '18 Reflection Effect - Definition 18

19 Reflection Effect (not a framing effect) Reflection Effect: People are generally risk averse for gains and risk seeking for losses. (This statement is generally true, although there are exceptions to it.) Example: Bettors at horse track bet on long shots at the end of the day (many are in a state of trying to recoup losses). By itself, reflection effect is not a framing effect (to be defined next), but it plays a role in preferences that exhibit framing effects. When the reflection effect is combined with changes in the framing of a choice (examples to be described next), it is possible to produce paradoxical patterns of preference that are called framing effects. Framing Effects Psych 355, Miyamoto, Spr '18 19

20 Framing Effects Definition: A framing effect has occurred if people s preferences change when: a) the description of the choice problem is changed, and... b) the content of the choice problem is not changed By content I mean the logical structure of the problem. If two problems are logically equivalent, they have the same content. The content is the same if different versions of the problem have the same probabilities and the same outcomes only the wording or "framing" of the problem changes. Basic Principle of Rational Choice: The framing of a problem should not affect the decisions of a rational agent (preference should not change as a function of problem description). When a framing effect is found, it is a violation of this principle of rational choice. Psych 355, Miyamoto, Spr '18 Comment on Goldstein's Definition of Framing Effects 20

21 Comment on Goldstein's Definition of "Framing Effects" Definition: A framing effect has occurred if people s preferences change when: a) the description of the choice problem is changed, and... b) the content of the choice problem is not changed Goldstein (p. 384) defines a framing effect only in terms of condition (a); he omitted any mention of condition (b). This omission is a mistake, i.e., my definition in terms of conditions (a) and (b) is better on theoretical grounds and it is closer to the usage of this term, "framing effect", in the literature of judgment and decision making. Psych 355, Miyamoto, Spr '18 Reflection Effects and Framing Effects 21

22 Wednesday, 30 May, 2018: The Lecture Ended Here Psych 355, Miyamoto, Spr '18 22

23 Psych 355, Miyamoto, Spr '18 23 Asian Disease Problem - Gain Frame Reflection Effects and Framing Effects By itself, a reflection effect is not a framing effect, but... reflection effects can be part of what causes a framing effect. How to create a framing effect: Change the wording of the choices to emphasize gains or to emphasize losses. Emphasize gains in the options Become more risk averse Emphasize losses in the options Become more risk seeking