Round Table and Panel Discussion The psychology of Mistakes American Academy of Appellate Lawyers

1. Round Table and Panel DiscussionThe psychology of MistakesAmerican Academy of Appellate Lawyers Massimo Piattelli-Palmarini Cognitive Science, University of Arizona March 24, 2006 Micro-irrationality

2. The coverage of this field • Articles relevant to this domain of research have been published in more than 400 scientific journals • There are, by now, over 20 extensive anthologies and several popularization books. • Including my own: • Massimo Piattelli-Palmarini (1994) Inevitable Illusions: How Mistakes of Reason Rule our Mind (John Wiley) • Courses in decision research are commonly taught to students in psychology, economics, philosophy, business, management, medicine, law, and in the military academies. Round Table on Errors

3. The coverage of this field • In the last several years, also cognitive neuroscientists have grown an interest in human decision making • Several papers have been published already on the brain “counterparts” of typical heuristics and biases. • Specific brain lesions have been discovered that selectively impair the decision-making ability of those patients (Antonio Damasio and collaborators at the University of Iowa) • The choices made by subjects in a particular game of cards (win/lose) is used as standard clinical diagnostic test to detect pathologically risk-prone subjects (compulsive gamblers etc.) Round Table on Errors

4. An important specification: • In this domain, we deal with problems and situations such that • It makes sense, and it is rather obvious • That there is such a thing as • The right decision, the correct choice, the correct answer, the correct estimate • We do not deal with fleeting propensities, mere tastes, personal inclinations, wanton impulses etc. • In this domain there are normative (rational) theories that do give the right answer • Our experimental subjects want to make the right choice, give the right answer Round Table on Errors

5. Names for this field • Behavioral Decision-Making • Psychology of reasoning • Psychology of choices • Decision research • Heuristics and Biases • Judgment and Decision-Making (JDM) • The latter is the most consolidated label • A Nobel Prize in economics changed it all Round Table on Errors

6. Heuristics • Form the Greek heurein = to find (whence the exclamation Eureka!) • Thumb-rules and intuitive strategies that we apply to the search for a solution in a certain class of problems. • Something we do • Consciously or unconsciously, or semi-consciously. • Heuristics have no secure warrant • That is, no rational warrant, • That is, they do not derive from first principles and logical proofs • Like full, guaranteed methods (and methodologies) do. Round Table on Errors

7. Biases • Tunnels of the mind • Of which we (usually) have no awareness • Something that happens to us • For instance (as we will see): • Anchoring • Partitions in probability estimates • Mental reference points and baselines • Ease of representation (availability) • And many more Round Table on Errors

8. Heuristics and biases • “neither rational, nor capricious” • A very synthetic characterization by Daniel Kahneman and Amos Tversky Round Table on Errors

9. Two giants of this field: • Amos Tversky (deceased in 1996, Stanford University) • Daniel Kahneman (Princeton University, Nobel Prize for Economics 2002) Daniel Kahneman Round Table on Errors

10. Daniel Kahneman receiving the Nobel Prize for Economics 2002 Round Table on Errors

11. Daniel Kahneman I recommend his Nobel Lecture Round Table on Errors

12. He would have shared the Nobel Prize with Kahneman, had he still been alive. Amos Tversky (1937-1996) Round Table on Errors

13. Rapid multiplication • Take a group of subjects, and subdivide it at random into two subgroups • Group A • You ask them to make a quick, approximate mental calculation of the following multiplication • 8765432 • Group B • You ask them to make a quick, approximate mental calculation of the following multiplication • 2345678 • What do you expect the results will be? Round Table on Errors

14. Rapid multiplication: The data • Group A: Average response = 2,250 for • 8765432 • Group B: Average response = 512 for • 2345678 • Exact result: 40,320 • No one guesses anywhere near the exact result. • Moreover • The two approximations are grossly different. • If you ask them, after they have given the estimate, • they all know the commutative property of multiplication! Round Table on Errors

15. The cognitive explanation: • Anchoring: You start multiplying left-to-right • Then extrapolate and round up • And you are “trapped” by what initially comes up, left to right • This is called an anchoring effect. • Many many examples in everyday life. • Notice: You have to work with two separate groups • Otherwise it’s impossible to reveal this effect with this rapid multiplication task. Round Table on Errors

16. Some ultra-simple examples:

17. The square turning into a rectangle • What is your intuition? Round Table on Errors

18. The normative solution • Since the perimeter is kept constant • The area cannot also be constant • In fact, it decreases monotonically to zero. L Area = L2 L Round Table on Errors

19. The normative solution • Since the perimeter is kept constant • The area cannot also be constant • In fact, it decreases monotonically to zero. x L + x Area = (L-x) • (L+x) = L2- x2 L-x Round Table on Errors

20. What happens in our mind: • A strong conservation principle is evoked: • Some portion of surface is added laterally • Some portion of surface is subtracted vertically • One side grows shorter • The other side grows longer • We (wrongly) infer that these variations compensate one another • And conclude that the surface is constant. Round Table on Errors

21. What happens next: • The surface goes to zero • Our intuition of conservation vacillates • Two reasoning strategies: • (1) Conservation prevails: • We introduce a “sudden” singularity • The surface is the same, until it vanishes at the limit (only at the limit) • (2) Continuity prevails • We abandon conservation, and accept that the surface must have been decreasing all the way • Notice: We do not accept contradictions and inconsistencies. We try to remedy, somehow. Round Table on Errors

22. Another very simple cognitive illusionThe two coins • Two coins are tossed into the air. I can see the result, but you cannot. I tell you truthfully that one of them has come up heads. What is the probability that the other also has come up heads? What do you say? • The vast majority answers: one half! • Why? • Two independent events (this is right) • “therefore” p=1/2 • (but this inference is wrong) • My report isnot about two independent events, but about a cumulative event. • The interesting cognitive fact is that we do not “see” it. Round Table on Errors

23. The problem of partitions • What can happen? • (a ) H H • (b ) H T • (c ) T H • (d ) T T • (d) is ruled out by my statement, therefore • p = 1/3 • A different situation: reporting about one specific coin, and asking about the other. We are blind to this difference: a cognitive oversight (neglect). Round Table on Errors

24. A real-life judicial episode • The O.J. Simpson Trial • The probability that a husband who batters his wife will end up murdering her is 1 in 2,500 (4 in ten thousand) (US Police records for 1992) • Imagine that you are a member of the jury. • Do you find this argument • Very convincing  • Somewhat convincing  • Only moderately relevant  • Totally irrelevant  Round Table on Errors

25. Confusing conditional probabilities • What is relevant is not the probability of murder, given beating • BUT • The probability that a wife who has been murdered, has been murdered by a partner who was known to beat her. • This is close to 90% • Also based on the same Police records • As remarked by I.J. Good in 1996, nobody pays any attention to this hugedifference in conditional probabilities. • Many, many examples in all walks of life Round Table on Errors

26. The maternity ward • A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day. In the smaller hospital about 15 babies are born each day. • As you know, about 50 per cent of all babies are girls. However, the exact percentage varies from day to day. • Sometimes it may be higher than 50 per cent, sometimes lower. Round Table on Errors

27. The maternity ward • For a period of one year, each hospital recorded the days on which 60 per cent or more of the babies born were girls. • Which hospital do you think recorded more such days? • Please indicate your choice: • The larger hospital � • The smaller hospital � • About the same � (within 5 per cent of each other) Round Table on Errors

28. The data • The larger hospital 22% • The smaller hospital 22% • About the same (within 5 per cent of each other) 56% • Rationale: Sex does not depend on the size of the hospital • Of course, but a fluctuation does • The correct answer is, in fact: The smaller hospital. Round Table on Errors

29. An interesting variant • Same story. But now the subjects are asked to estimate which hospital recorded more days in which all the babies were girls. • Now over 90% of subjects choose the smaller hospital. • Many re-consider their previous intuition • But some don’t. • Notice: Those who reconsidered have not been “instructed”. Only questioned. • The de-biasing is a self-de-biasing. Round Table on Errors

30. If that be madness…….. • Indeed, these heuristics and biases are “neither rational, nor capricious” (Amos Tversky and Daniel Kahneman) • These effects are: • Systematic • Resistant to “de-biasing” • Stimuli for improvised “rationalizations” • Independent of the level of education • (Presumably) culture-independent Round Table on Errors

31. An important lesson: • We knew all along that people are “irrational” • Sure! • Because of passions, selfishness, greed, ambition, racism, prejudice, sheer stupidity, superstition, etc. • None of the above factors is involved in the problems we treat in this domain. • This is a different kind of irrationality. • I have called it micro-irrationality • Only systematic, predictable errors of intuition and reasoning. • This is what I have also called the “cognitive unconscious” (see my 1994 book Inevitable Illusions, Wiley). Round Table on Errors

32. Monty Hall Paradox*1 Round Table on ErrorsTradeoff Studies ver 4

33. Monty Hall Paradox*2 Round Table on ErrorsTradeoff Studies ver 4

34. Monty Hall Paradox*3 Round Table on ErrorsTradeoff Studies ver 4

35. Monty Hall Paradox*4 Round Table on ErrorsTradeoff Studies ver 4

36. Monty Hall Paradox*5 • Now here is your problem. • Are you better off sticking to your original choice or switching? • A lot of people say it makes no difference. • There are two boxes and one contains a ten-dollar bill. • Therefore, your chances of winning are 50/50. • However, the laws of probability say that you should switch. Round Table on ErrorsTradeoff Studies ver 4

37. Monty Hall Paradox6 • The box you originally chose has, and always will have, a one-third probability of containing the ten-dollar bill. • The other two, combined, have a two-thirds probability of containing the ten-dollar bill. • But at the moment when I open the empty box, then the other one alone will have a two-thirds probability of containing the ten-dollar bill. • Therefore, your best strategy is to always switch! Round Table on ErrorsTradeoff Studies ver 4

38. Christopher K. Hsee (University of Chicago) (1998) Group 1 How much would you offer for an ice-cream cup like the above, of your favorite flavor? Round Table on Errors

39. Group 2 How much for this cup (again, of your favorite flavor)? Round Table on Errors

40. Group 3 Vendor L is more attractive for a majority of subjects tested separately. Round Table on Errors

41. Hardly anyone prefers vendor L when both drawings are shown (As they are here) (Group 3) Round Table on Errors

42. Explanation • The reference point is very important • An overflowing amount in a smaller cup is “a lot” of ice cream • A partially un-filled amount in a larger cup is not “a lot” • S. Dehaene and L. Cohen (1991) have discoverd two distinct cerebral areas • One for “gross approximations” • One for precise calculations • Selective brain lesions actually disrupt one, but not the other Round Table on Errors

43. Preferences for a safety apparatusin airports (Paul Slovic, 2003) • How intensely would you endorse a new safety device, knowing that: • Group A: It can save the lives of 150 people • Group B: It can save 98% of human lives, over a total of 150 people. • The rating ranges from 0 (no endorsement) to 20 (very enthousiastic endorsement) • A (as an average) 10.4 • B (as an average) 13.6 Round Table on Errors

44. Same question (Paul Slovic, 2003) • Group C: Can save 95% of human lives, over a total of 150 people • Group D: 90% • Group E: 85% • C (average) 12.9 • D (average) 11.7 • E (average) 10.9 • Reminder: A was 10.4 (for allthe 150 people) Round Table on Errors

45. Percentage of sanguine endorsement (Paul Slovic, 2003) • Percentage of responses higher than 13 (sanguine endorsement), per group : • A (150 people) 37% • B (98% of 150) 75% • C (95% of 150) 69% • D (90% of 150) 35% • E (85% of 150) 31% • Saving fewer lives, with respect to A, receives greater endorsement and more “enthousiastic” endorsement. • Why? Round Table on Errors

46. Explanation: • Just like for the ice cream, • 150 people is an « open » datum (Is it “a lot”? Is it “too few”?). • Hard to tell. • But 98% of 150 people is a lot! • With respect to the explicit « roof » of 100% • You like this! • And you endorse the proposal more intensely. Round Table on Errors

47. A field called probabilistic judgment • Recipe: • Take one of the axioms of normative probability calculus. • You have reasons to suspect that people often violate it • Design a cute experiment • Publish a paper showing that a majority of subjects violate that axiom • Choose another axiom • Repeat the above procedure • Construct your favorite cognitive theory of spontaneous probability judgments. Round Table on Errors

48. Standard example • Axiom: p(e) = 1-p(e) • Violation: Zeckhauser and the forcible Russian Roulette: • How much would you be willing to pay to remove one bullet from the drum? • From 1 bullet to zero • From 4 bullets to 3 • From 6 bullets to 5 • A steeply decreasing function from both extremes. • 1/6 of increase in the probability of survival is worth a lot if it is from 5/6 to one, and from zero to 1/6, not much if it is from 2/6 to 3/6 • Sensitivity to differences increases sharply near the endpoints. Round Table on Errors

49. x 2.5x A typical subjective value function: Notice the 2.5 asymmetry between gains and losses Round Table on Errors

50. A standard test: Choices between lotteries • What would you prefer: $100 for sure or $1,000 with probability 10% • A long series of well-calibrated choices between pairs of lotteries • One with low gain and high probability • One with high gain and low probability • We measure a function of objective probabilities • The subjective probability weights • How much a probability p “weighs” on that person’s decisions w(p) • The shape of the curve is universal, and it’s quite interesting Round Table on Errors