Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 10. Behavioral Biases II Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 1 / 23
Introduction Overview The Conjunction Fallacy Stereotypes Regression to the Mean The Halo E¤ect Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 2 / 23
The Conjunction Fallacy Consider the following description (apologies for the somewhat outdated example): Linda is thirty-one old, single, outspoken, and very bright.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 antinuclear demonstrations. Now rank the following scenarios for Linda by probability. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 3 / 23
The Conjunction Fallacy Linda is a teacher in elementary school. Linda works in a bookstore and takes yoga classes. Linda is active in the feminist movement. Linda is a psychiatric social worker. Linda is a member of the League of Women Voters. Linda is a bank teller. Linda is an insurance salesperson. Linda is a bank teller and is active in the feminist movement. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 4 / 23
The Conjunction Fallacy Obviously, Linda …ts the idea of a “feminist bank teller”. Adding the detail “feminist” to the scenario makes for a more coherent story. However, by the rules of pure logic, the probability that Linda is a feminist bank teller must be smaller than the probability that Linda is a bank teller. Nevertheless, a large majority of subjects (e.g. students from Stanford Graduate School of Business), between 80% and 90%, ranked “feminist bank teller” as more likely than “bank teller”. The systematic violation of the conjunction rule is called conjunction fallacy . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 5 / 23
The Conjunction Fallacy The conjunction fallacy is quite robust. It does not disappear if one reduces the set of scenarios to the relevant two ones: Linda is a bank teller. Linda is a bank teller and is active in the feminist movement. Now 35% of the student subjects fall prey to the conjunction fallacy. In order to appreciate the role of plausibility, consider the following question: Which alternative is more probable? Mark has hair. Mark has blond hair. This question does not cause a fallacy, because the more detailed outcome is not more plausible. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 6 / 23
The Conjunction Fallacy Estimate the value of these two sets of dinnerware: Set A : 40 pieces Set B : 24 pieces Dinner plates 8, all in good condition 8, all in good condition Salad bowls 8, all in good condition 8, all in good condition Dessert plates 8, all in good condition 8, all in good condition Cups 8, 2 of them are broken 0 Saucers 8, 7 of them are broken 0 Set A must be valued more. If subjects can compare the two sets (within-subject), they are indeed willing to pay a little more for A than for B (32 USD and 30 USD, respectively). But what happens if each subject only evaluates one of the two sets (between-subjects)? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 7 / 23
The Conjunction Fallacy Under single evaluation, set B was priced much higher than set A : 33 USD versus 23 USD. It seems that subjects price the sets according to the average value of the dishes (which of course is lower for set A ). Sets are represented by norms and prototypes. From an economic perspective, this result is troubling for theory: the economic value of a collection of items is a sum-like variable. Adding a positively valued item to the set can only increase its value. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 8 / 23
The Conjunction Fallacy In order to avoid the objection that the conjunction fallacy is caused by a misinterpretation of probability, the following experiment has been conducted. There is a six-sided dice with four green and two red faces, which would be rolled 20 times. Subjects were shown three sequences of greens and reds, and were asked to choose one: 1. RGRRR 2. GRGRRR 3. GRRRRR They would win 25 USD if their chosen sequence showed up. What sequence would/should subjects choose? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 9 / 23
The Conjunction Fallacy The second sequence is constructed from the …rst by adding a G . So the second sequence is less likely to show up than the …rst one. However, the second sequence looks more representative than the …rst, because it contains more G s. Indeed, two-thirds of respondents choose the second sequence. Hence, the conjunction fallacy is not due to a misinterpretation of the term probability. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 10 / 23
Stereotypes Consider the following scenario. A cab was involved in a hit-and-run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data: 1. 85% of the cabs in the city are Green and 15% are Blue. 2. A witness identi…ed the cab as Blue. The court tested the reliability of the witness under the circumstances that existed on the night of the accident and concluded that the witness correctly identi…ed each one of the two colors 80% of the time and failed 20% of the time. What is the probability that the cab involved in the accident was Blue rather than Green? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 11 / 23
Stereotypes Obviously, this is a Bayesian Inference problem and the correct answer is 0 , 15 � 0 , 80 P ( color = b j witness = b ) = 0 , 85 � 0 , 20 + 0 , 15 � 0 , 80 � 0 , 41 . Perhaps not surprisingly, people mostly ignore the base rate and go with the witness. The common answer is 80%. Now consider the same question except that the information 85% of the cabs in the city are Green and 15% are Blue. is substituted by The two companies operate the same number of cabs, but Green cabs are involved in 85% of accidents. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 12 / 23
Stereotypes The two versions of the problem are mathematically identical. However, while people often ignore the statistical information in the …rst version, they give considerable weight to the base rate in the second version. The second version of the problem creates a stereotype : Drivers of the green company are reckless madmen! The stereotype is easily …tted into a causal story. The inferences of the two stories are contradictory and approximately cancel each other. Hence, subjects come up with a much better estimate under the second version of the problem (around 50%). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 13 / 23
Stereotypes Many experiments con…rm the following …ndings. Statistical base rates are generally underweighted, and sometimes neglected altogether, when speci…c information about the case at hand is available. Causal base rates (created by stereotypes) are treated as information about the individual case and are easily combined with other case-speci…c information. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 14 / 23
Stereotypes Stereotypes, both correct and false, are how we think of categories. We consider it morally desirable for base rates to be treated as statistical fact about the group rather than as presumptive facts about individuals. In other words: There is a strong social norm against stereotyping. However, as we just saw, causal base rates/stereotypes may improve probability judgments! Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 15 / 23
Regression to the Mean Outcomes in many domains such as business and sports are determined by two factors, talent and luck. This causes regression to the mean : if a variable (pro…t, scores) is extreme on its …rst measurement, it will tend to be closer to the average on its second measurement (and vice versa). Whenever the correlation between two scores is imperfect, there will be regression to the mean. However, our mind is strongly biased toward causal explanations and does not deal well with statistics. So the phenomenon of regression is quite strange to the human mind. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 16 / 23
Regression to the Mean Consider the following proposition: Highly intelligent women tend to marry men who are less intelligent than they are. Most people will spontaneously interpret the statement in causal terms (i.e., they come up with a story that explains this phenomenon). The following statement is algebraically equivalent, but far less interesting for most people. The correlation between the intelligence scores of spouses is less than perfect. If the correlation between the intelligence of spouses is less than perfect, it is a mathematical inevitability that highly intelligent women will be married to husbands who are on average less intelligent than they are. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 10. Behavioral Biases II 17 / 23
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