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Incentives and Behavior Prof. Dr. Heiner Schumacher KU Leuven 9. Behavioral Biases I Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 1 / 36

Introduction Literature Kahneman, Daniel (2011): Thinking, Fast and Slow , Farrar, Straus and Giroux, New York, Part 2 (“Heuristics and Biases”). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 2 / 36

Introduction In the last chapters, we discussed human preferences . “De gustibus non est disputandum.” Now we turn to behavioral biases . Behavioral biases (or decision errors) are behaviors that people would not exhibit if they would examine the situation with su¢cient care. From a welfare-economics perspective the existence of biases is problematic. If many individuals exhibit biased decision making, there could be scope for public policy that helps them to make better decisions. Most of the material we consider in the following is due to the psychologists Daniel Kahneman and Amos Tversky. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 3 / 36

Introduction Overview The Law of Small Numbers Anchors Availability Availability and Risk Representativeness Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 4 / 36

The Law of Small Numbers The Law of Large Numbers. Let x 1 , x 2 , ... be an in…nite sequence of independent and identically distributed random variables with expected value E ( x i ) = µ for all i . Then the sample average X n = 1 ¯ n ( x 1 + ... + x n ) converges to the expected value: ¯ X n ! µ for n ! ∞ . Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 5 / 36

The Law of Small Numbers Many people (scientists and non-scientists alike) exaggerate how likely it is that a small sample resembles the population from which it is drawn. This phenomenon is called the belief in the “law of small numbers”. The …rst study on this subject is Tversky and Kahneman (1971). They …nd that even mathematical psychologists greatly overestimate the likelihood that results that have been found signi…cant in small samples (e.g. 20 subjects) remain signi…cant when the sample size is doubled. 1 The belief in the law of small numbers can lead to severe decision errors. 1 Tversky, Amos, and Daniel Kahneman (1971): “Belief in the law of small numbers,” Psychological Bulletin 76(2), 105 - 110. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 6 / 36

The Law of Small Numbers As an illustration, take the sex of six babies born in sequence at a hospital. Obviously, the sequence of boys ( B ) and girls ( G ) is random and the events are independent from each other. Consider the following three possible sequences: BBBGGG GGGGGG BGBBGB Are these sequences equally likely? Which sequence is the most likely one? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 7 / 36

The Law of Small Numbers Random processes produce many sequences that convince people that the process is not random after all. Consequently, people are very bad at producing random sequences. For example, Rapoport and Budescu (1997) asked their subjects to “imagine a sequence of 150 draws with replacement from a well-shu-ed deck, including …ve red and …ve black cards, and then call aloud the sequence of these binary draws”. 2 The probability that a subject would produce a signal given that the previous 0, 1, 2, or 3+ signals chosen were that same signal were as follows: 3 Pr ( A j B ) 58 . 5 % Pr ( A j AB ) 46 . 0 % Pr ( A j AAB ) 38 . 0 % Pr ( A j AAA ... ) 29 . 8 % 2 Rapoport, Amnon, and David V. Budescu (1997): “Randomization in individual choice behavior,” Psychological Review 104(3), 603 - 617. 3 These numbers are taken from Rabin (2002). Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 8 / 36

The Law of Small Numbers A phenomenon that is related to beliefs in the law of small numbers is the hot hand fallacy : If there is uncertainty about the data generating process, then many people treat even short random sequences as highly representative of the random process. Gilovich et al. (1985) show (irrational) beliefs in the hot hand in basketball. 4 Players and fans alike tend to believe that a player’s chance of scoring are greater following a hit than following a miss on the previous shot. However, the correlation between outcomes of successive shots is zero. Camerer (1989) shows that the belief in the hot hand may have an in‡uence on betting odds. 5 4 Gilovich, Thomas, Robert Vallone, and Amos Tversky (1985): “The hot hand in basketball: On the misperception of random sequences,” Cognitive Psychology 17(3), 295 - 314. 5 Camerer, Colin (1989): “Does the basketball market believe in the hot hand?,” American Economic Review 79(5), 1257 - 1261. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 9 / 36

The Law of Small Numbers Do beliefs in the law of small numbers a¤ect important decisions? There is some evidence that the answer is yes. The Gates Foundation invested 1.7 billion USD in order to …nd out the characteristics of the most successful schools. The critical measures were math and reading skills in several grades. One conclusion from this research was that most successful schools, on average, are small. For example, in Pennsylvania, 6 of the top 50 were small (an overrepresentation by a factor of 4). This encouraged the Gates Foundation (and a large number of other prominent organizations) to invest a lot of money in order to split up large schools in smaller units. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 10 / 36

The Law of Small Numbers It is easy to construct a story that explains why small schools perform better than larger ones. However, if one asks about the characteristics of the worst schools, one also …nds a overrepresentation of small schools (by the same factor). Small schools are not better than large schools; the test scores are just more variable. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 11 / 36

Anchors Consider the following experiment. In the …rst stage, the subject spins a wheel of fortune that may stop either at 10 or at 65. She then has to write down this number. In the second stage, the subject has two answer the following two questions: Is the percentage of African nations among UN members larger or smaller than the number you just wrote? What is your best guess of the percentage of African nations in the UN? Does the random number from the …rst stage in‡uence the answers in the second stage of the experiment? Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 12 / 36

Anchors The average estimate of those who saw 10 were 25% and that of those who saw 65 was 45%. This phenomenon is called anchoring . It occurs when people consider a particular value for an unknown quantity before estimating that quantity. The estimates on average stay close the number people considered. Anchoring is one of the most reliable and robust results of experimental psychology. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 13 / 36

Anchors There are two psychological processes that lead to anchoring. The …rst is insu¢cient adjustment . Start from an anchoring number, assess whether it is too high or too low, and gradually adjust your estimate by mentally “moving” from the anchor. Insu¢cient adjustment operates at questions like the following one: What is the boiling temperature of water at the top of Mount Everest? An anchor comes immediately to your mind (100 � C ) from which you adjust downwards (because you know that the boiling temperature must be lower). On average, the adjustment process stops too early. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 14 / 36

Anchors The second process is priming. Priming is the temporary activation of an individual’s mental representations (ideas) and the e¤ect of this activation on behavior in an unrelated subsequent task. As an illustration, consider the following question. Was Gandhi more or less than 144 years old when he died? How old was Gandhi when he died? It does not make sense to adjust the age downwards from 144. However, it creates the image of a very old person. On the contrary, if 144 is substituted by a very low number, say 12, this creates the image of a very young person. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 15 / 36

Anchors Unlike many other biases, anchoring can be measured. Consider the following question. Is the height of the tallest redwood more or less than X feet? What is your best guess about the height (in feet) of the tallest redwood? Let X H = 1200 be the “high anchor” and X L = 180 the “low anchor”. The high anchor produces an average estimate of Y H = 844, while the low anchor produces an average estimate of Y L = 282. The anchoring index is de…ned by anchoring _ index = Y H � Y L %. X H � X L In the current example, the anchoring index equals 55 % , a typical number for many anchoring results. Prof. Dr. Heiner Schumacher (KU Leuven) Incentives and Behavior 9. Behavioral Biases I 16 / 36