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Round Table and Panel Discussion The psychology of Mistakes American Academy of Appellate Lawyers Massimo Piattelli-Palmarini Cognitive Science, University of Arizona March 24, 2006 Micro-irrationality

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UofA March 24 2006Round Table on Errors The coverage of this field n Articles relevant to this domain of research have been published in more than 400 scientific journals n There are, by now, over 20 extensive anthologies and several popularization books. n Including my own: n Massimo Piattelli-Palmarini (1994) Inevitable Illusions: How Mistakes of Reason Rule our Mind (John Wiley) n Courses in decision research are commonly taught to students in psychology, economics, philosophy, business, management, medicine, law, and in the military academies.

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UofA March 24 2006Round Table on Errors The coverage of this field n In the last several years, also cognitive neuroscientists have grown an interest in human decision making n Several papers have been published already on the brain counterparts of typical heuristics and biases. n 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) n 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.)

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UofA March 24 2006Round Table on Errors An important specification: n In this domain, we deal with problems and situations such that n It makes sense, and it is rather obvious n That there is such a thing as n The right decision, the correct choice, the correct answer, the correct estimate n We do not deal with fleeting propensities, mere tastes, personal inclinations, wanton impulses etc. n In this domain there are normative (rational) theories that do give the right answer n Our experimental subjects want to make the right choice, give the right answer

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UofA March 24 2006Round Table on Errors Names for this field n Behavioral Decision-Making n Psychology of reasoning n Psychology of choices n Decision research n Heuristics and Biases n Judgment and Decision-Making (JDM) n The latter is the most consolidated label n A Nobel Prize in economics changed it all

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UofA March 24 2006Round Table on Errors Heuristics n Form the Greek heurein = to find (whence the exclamation Eureka!) n Thumb-rules and intuitive strategies that we apply to the search for a solution in a certain class of problems. n Something we do n Consciously or unconsciously, or semi- consciously. n Heuristics have no secure warrant n That is, no rational warrant, n That is, they do not derive from first principles and logical proofs n Like full, guaranteed methods (and methodologies) do.

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UofA March 24 2006Round Table on Errors Biases n Tunnels of the mind n Of which we (usually) have no awareness n Something that happens to us n For instance (as we will see): n Anchoring n Partitions in probability estimates n Mental reference points and baselines n Ease of representation (availability) n And many more

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UofA March 24 2006Round Table on Errors Heuristics and biases nneither rational, nor capricious n A very synthetic characterization by Daniel Kahneman and Amos Tversky

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UofA March 24 2006Round Table on Errors Two giants of this field: n Amos Tversky (deceased in 1996, Stanford University) n Daniel Kahneman (Princeton University, Nobel Prize for Economics 2002) Daniel Kahneman

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UofA March 24 2006Round Table on Errors Daniel Kahneman receiving the Nobel Prize for Economics 2002

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UofA March 24 2006Round Table on Errors Daniel Kahneman I recommend his Nobel Lecture

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UofA March 24 2006Round Table on Errors Amos Tversky He would have shared the Nobel Prize with Kahneman, had he still been alive. (1937-1996)

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UofA March 24 2006Round Table on Errors Rapid multiplication n Take a group of subjects, and subdivide it at random into two subgroups n Group A n You ask them to make a quick, approximate mental calculation of the following multiplication n 8 7 6 5 4 3 2 n Group B n You ask them to make a quick, approximate mental calculation of the following multiplication n 2 3 4 5 6 7 8 n What do you expect the results will be?

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UofA March 24 2006Round Table on Errors Rapid multiplication: The data n Group A: Average response = 2,250 for n 8 7 6 5 4 3 2 n Group B: Average response = 512 for n 2 3 4 5 6 7 8 n Exact result: 40,320 n No one guesses anywhere near the exact result. n Moreover n The two approximations are grossly different. n If you ask them, after they have given the estimate, n they all know the commutative property of multiplication!

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UofA March 24 2006Round Table on Errors The cognitive explanation: n Anchoring: You start multiplying left-to-right n Then extrapolate and round up n And you are trapped by what initially comes up, left to right n This is called an anchoring effect. n Many many examples in everyday life. n Notice: You have to work with two separate groups n Otherwise its impossible to reveal this effect with this rapid multiplication task.

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Some ultra-simple examples:

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UofA March 24 2006Round Table on Errors The square turning into a rectangle n What is your intuition?

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UofA March 24 2006Round Table on Errors The normative solution n Since the perimeter is kept constant n The area cannot also be constant n In fact, it decreases monotonically to zero. L L Area = L 2

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UofA March 24 2006Round Table on Errors The normative solution n Since the perimeter is kept constant n The area cannot also be constant n In fact, it decreases monotonically to zero. L-x L + x Area = (L-x) (L+x) = L 2 - x 2 x

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UofA March 24 2006Round Table on Errors What happens in our mind: n A strong conservation principle is evoked: n Some portion of surface is added laterally n Some portion of surface is subtracted vertically n One side grows shorter n The other side grows longer n We (wrongly) infer that these variations compensate one another n And conclude that the surface is constant.

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UofA March 24 2006Round Table on Errors What happens next: n The surface goes to zero n Our intuition of conservation vacillates n Two reasoning strategies: n (1) Conservation prevails: n We introduce a sudden singularity n The surface is the same, until it vanishes at the limit (only at the limit) n (2) Continuity prevails n We abandon conservation, and accept that the surface must have been decreasing all the way n Notice: We do not accept contradictions and inconsistencies. We try to remedy, somehow.

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UofA March 24 2006Round Table on Errors Another very simple cognitive illusion The two coins n 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? n The vast majority answers: one half! n Why? n Two independent events (this is right) n therefore p=1/2 n (but this inference is wrong) n My report is not about two independent events, but about a cumulative event. n The interesting cognitive fact is that we do not see it.

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UofA March 24 2006Round Table on Errors The problem of partitions n What can happen? n (a ) H H n (b ) H T n (c ) T H n (d ) T T n (d) is ruled out by my statement, therefore n p = 1/3 n A different situation: reporting about one specific coin, and asking about the other. We are blind to this difference: a cognitive oversight (neglect).

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UofA March 24 2006Round Table on Errors A real-life judicial episode n The O.J. Simpson Trial n 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) n Imagine that you are a member of the jury. n Do you find this argument u Very convincing u Somewhat convincing u Only moderately relevant u Totally irrelevant

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UofA March 24 2006Round Table on Errors Confusing conditional probabilities n What is relevant is not the probability of murder, given beating n BUT n The probability that a wife who has been murdered, has been murdered by a partner who was known to beat her. n This is close to 90% n Also based on the same Police records n As remarked by I.J. Good in 1996, nobody pays any attention to this huge difference in conditional probabilities. n Many, many examples in all walks of life

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UofA March 24 2006Round Table on Errors The maternity ward n 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. n As you know, about 50 per cent of all babies are girls. However, the exact percentage varies from day to day. n Sometimes it may be higher than 50 per cent, sometimes lower.

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UofA March 24 2006Round Table on Errors The maternity ward n For a period of one year, each hospital recorded the days on which 60 per cent or more of the babies born were girls. n Which hospital do you think recorded more such days? n Please indicate your choice: The larger hospital The smaller hospital About the same (within 5 per cent of each other)

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UofA March 24 2006Round Table on Errors The data u The larger hospital 22% u The smaller hospital 22% u About the same (within 5 per cent of each other) 56% n Rationale: Sex does not depend on the size of the hospital n Of course, but a fluctuation does n The correct answer is, in fact: The smaller hospital.

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UofA March 24 2006Round Table on Errors An interesting variant n Same story. But now the subjects are asked to estimate which hospital recorded more days in which all the babies were girls. n Now over 90% of subjects choose the smaller hospital. n Many re-consider their previous intuition n But some dont. n Notice: Those who reconsidered have not been instructed. Only questioned. n The de-biasing is a self-de-biasing.

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UofA March 24 2006Round Table on Errors If that be madness…….. n Indeed, these heuristics and biases are neither rational, nor capricious (Amos Tversky and Daniel Kahneman) n These effects are: u Systematic u Resistant to de-biasing u Stimuli for improvised rationalizations u Independent of the level of education u (Presumably) culture-independent

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UofA March 24 2006Round Table on Errors An important lesson: n We knew all along that people are irrational n Sure! n Because of passions, selfishness, greed, ambition, racism, prejudice, sheer stupidity, superstition, etc. n None of the above factors is involved in the problems we treat in this domain. n This is a different kind of irrationality. n I have called it micro-irrationality n Only systematic, predictable errors of intuition and reasoning. n This is what I have also called the cognitive unconscious (see my 1994 book Inevitable Illusions, Wiley).

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 Monty Hall Paradox * 1

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 Monty Hall Paradox * 2

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 Monty Hall Paradox * 3

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 Monty Hall Paradox * 4

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 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.

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6/13/2014Round Table on ErrorsTradeoff Studies ver 4 Monty Hall Paradox 6 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!

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UofA March 24 2006Round Table on Errors How much would you offer for an ice-cream cup like the above, of your favorite flavor? Christopher K. Hsee (University of Chicago) (1998) Group 1

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UofA March 24 2006Round Table on Errors How much for this cup (again, of your favorite flavor)? Group 2

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UofA March 24 2006Round Table on Errors Vendor L is more attractive for a majority of subjects tested separately. Group 3

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UofA March 24 2006Round Table on Errors Hardly anyone prefers vendor L when both drawings are shown (As they are here) (Group 3)

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UofA March 24 2006Round Table on Errors Explanation n The reference point is very important n An overflowing amount in a smaller cup is a lot of ice cream n A partially un-filled amount in a larger cup is not a lot n S. Dehaene and L. Cohen (1991) have discoverd two distinct cerebral areas n One for gross approximations n One for precise calculations n Selective brain lesions actually disrupt one, but not the other

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UofA March 24 2006Round Table on Errors Preferences for a safety apparatus in airports (Paul Slovic, 2003) n How intensely would you endorse a new safety device, knowing that: n Group A: It can save the lives of 150 people n Group B: It can save 98% of human lives, over a total of 150 people. n The rating ranges from 0 (no endorsement) to 20 (very enthousiastic endorsement) n A (as an average) 10.4 n B (as an average) 13.6

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UofA March 24 2006Round Table on Errors Same question (Paul Slovic, 2003) n Group C: Can save 95% of human lives, over a total of 150 people n Group D: 90% n Group E: 85% n C (average) 12.9 n D (average) 11.7 n E (average) 10.9 n Reminder: A was 10.4 (for all the 150 people)

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UofA March 24 2006Round Table on Errors Percentage of sanguine endorsement (Paul Slovic, 2003) n Percentage of responses higher than 13 (sanguine endorsement), per group : n A (150 people) 37% n B (98% of 150) 75% n C (95% of 150) 69% n D (90% of 150)35% n E (85% of 150) 31% n Saving fewer lives, with respect to A, receives greater endorsement and more enthousiastic endorsement. n Why?

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UofA March 24 2006Round Table on Errors Explanation: n Just like for the ice cream, n 150 people is an « open » datum (Is it a lot? Is it too few?). n Hard to tell. n But 98% of 150 people is a lot! n With respect to the explicit « roof » of 100% n You like this! n And you endorse the proposal more intensely.

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UofA March 24 2006Round Table on Errors A field called probabilistic judgment n Recipe: n Take one of the axioms of normative probability calculus. n You have reasons to suspect that people often violate it n Design a cute experiment n Publish a paper showing that a majority of subjects violate that axiom n Choose another axiom n Repeat the above procedure n Construct your favorite cognitive theory of spontaneous probability judgments.

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UofA March 24 2006Round Table on Errors Standard example n Axiom: p( e) = 1-p(e) n Violation: Zeckhauser and the forcible Russian Roulette: n How much would you be willing to pay to remove one bullet from the drum? n From 1 bullet to zero n From 4 bullets to 3 n From 6 bullets to 5 n A steeply decreasing function from both extremes. n 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 n Sensitivity to differences increases sharply near the endpoints.

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UofA March 24 2006Round Table on Errors A typical subjective value function: Notice the 2.5 asymmetry between gains and losses x 2.5x

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UofA March 24 2006Round Table on Errors A standard test: Choices between lotteries n What would you prefer: $100 for sure or $1,000 with probability 10% n A long series of well-calibrated choices between pairs of lotteries n One with low gain and high probability n One with high gain and low probability n We measure a function of objective probabilities n The subjective probability weights n How much a probability p weighs on that persons decisions w(p) n The shape of the curve is universal, and its quite interesting

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UofA March 24 2006Round Table on Errors Data from Tversky and Kahneman 1992

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UofA March 24 2006Round Table on Errors The behavior of W(p) for very low probabilities Drazen Prelec (2000) in a thousand zone in ten thousands zone in a million zone in 100 thousands zone

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UofA March 24 2006Round Table on Errors The behavior of W(p) for very low probabilities Notice that the weighting function becomes flatter and flatter. One chance in a million is the same as 2 or 3 chances in a million in a thousand zone in ten thousands zone in a million zone in 100 thousands zone

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UofA March 24 2006Round Table on Errors This shape reflects the all-or-none character of perceived risk The weighting function becomes flatter and flatter. BUT the transition from exactly zero to even very small probabilities is HUGE

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UofA March 24 2006Round Table on Errors As we know all too well n The total cancellation of a small risk is hugely over-rated n Even for a very, very, very small risk (one in a million) n WHILE n The mere reduction of that same risk n (from, say, ten in a million to one in a million) n is vastly under-rated. n Risk, in the popular mind, is something that is there or is not there (a quantum perception) n The slope of W(p) at zero is, in fact, infinite

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UofA March 24 2006Round Table on Errors Typical values n W(0.5) ~ 0.4 n W(0.25) ~ 0.3 n 1.33 times W(0.5)/2 n W(0.05) ~ 0.15 n 2.7 times W(0.5)/10 n As probabilities decrease, the gap widens in a spectacular way n W(0.005) ~ 0.075 n 15 times W(0.5)/10

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UofA March 24 2006Round Table on Errors Some consequences n Most of us are risk-averse for gains and risk- seekers for losses n We tend to evaluate gains separately from losses n We over-weigh small probabilities n And under-weigh large probabilities u The dividing point is about 37% u We are well calibrated around that point n Different ways of truthfully presenting the same options can have dramatic effects on decision-making and preferences n This effects are called framing effects

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UofA March 24 2006Round Table on Errors General culture questions n In each of the following pairs, which city has more inhabitants? n (a) Las Vegas (b) Miami n (a) Sydney (b) Melbourne n (a) Hyderabad (b) Islamabad n (a) Bonn (b) Heidelberg

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UofA March 24 2006Round Table on Errors How do we answer? n Recollection of facts we remember, and of scraps of information from various sources n Contingent pieces of information: n This city name is quite familiar (unfamiliar) to me n My cousin visited this city n Its a capital (or is not a capital) n This one has a famous University (soccer team, arts festival, etc.), but not the other. n Fame and familiarity usually go with the size of the city.

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UofA March 24 2006Round Table on Errors The brute facts: n These are the real data (rounded up): n (a) Las Vegas (b) Miami n 600,000 370,000 n (a) Sydney (b) Melbourne n 4 millions 1 million n (a) Hyderabad (b) Islamabad n 5.2 millions 900,000 n (a) Bonn (b) Heidelberg n 297,000 140,000

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UofA March 24 2006Round Table on Errors Over-confidence n After each answer subjects are also asked: n How confident are you that your answer is correct? n 50% 60% 70% 80% 90% 100% n It is typical to find that for the cases in which subjects say they are 100% confident, only about 80% of their answers are correct; n for cases in which they say that they are 90% confident, only about 70% of their answers are correct; n and for cases in which they say that they are 80% confident, only about 60% of their answers are correct.

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UofA March 24 2006Round Table on Errors Over-confidence n This tendency toward overconfidence seems to be very robust. n Warning subjects that people are often overconfident has no significant effect, nor does offering them money (or other material incentives) as a reward for accuracy. n Moreover, the phenomenon has been demonstrated in a wide variety of subject populations including undergraduates, graduate students, physicians, physicists and even CIA analysts. (Lichtenstein, Fischhoff & Phillips, 1982.)

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UofA March 24 2006Round Table on Errors Experienced horse handicappers making predictions on specific horses for specific races (Paul Slovic, 1973) Overconfidence

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UofA March 24 2006Round Table on Errors On overconfidence n In their domain of expertise, subjects are more accurate n But the increase in their over-confidence exceeds by far the increase in accuracy. n They are over-confident where they can do most damage

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UofA March 24 2006Round Table on Errors A knock-down objection, and a conclusion: n Bertrand Russell, one of the greatest logicians and philosophers of all times n And a great rationalist, wrote: n It is a dangerous and self-destructive folly to think that, since reason is not sufficient, then it is not necessary. n In other words: n We do not always have to decide rationally, in every matter n But n When we intend to make a rational decision n Then, it better be rational.

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