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

Round Table and Panel Discussion The psychology of MistakesAmerican Academy of Appellate Lawyers

Massimo Piattelli-PalmariniCognitive Science, University of Arizona

March 24, 2006

Micro-irrationality

UofA March 24 2006 Round Table on Errors

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.


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.)


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


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


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.


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


Heuristics and biases

“neither rational, nor capricious” A very synthetic characterization by Daniel

Kahneman and Amos Tversky


Two giants of this field:

Amos Tversky (deceased in 1996, Stanford University)

Daniel Kahneman (Princeton University, Nobel Prize for Economics 2002)

Daniel Kahneman


Daniel Kahnemanreceiving theNobel Prize forEconomics 2002


Daniel Kahneman

I recommend his Nobel Lecture


Amos TverskyHe would haveshared the NobelPrize withKahneman, hadhe still beenalive.

(1937-1996)


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 8765432

Group B You ask them to make a quick, approximate

mental calculation of the following multiplication 2345678

What do you expect the results will be?


Rapid multiplication: The data Group A: Average response = 2,250 for

8765432 Group B: Average response = 512 for

2345678 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!


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.

Some ultra-simple examples:


The square turning into a rectangle

What is your intuition?


The normative solution

Since the perimeter is kept constant The area cannot also be constant In fact, it decreases monotonically to zero.

L

L

Area = L2


The normative solution

Since the perimeter is kept constant The area cannot also be constant In fact, it decreases monotonically to zero.

L-x

L + x

Area = (L-x) • (L+x) = L2- x2

x


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.


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.


Another very simple cognitive illusion The 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 is not about two independent events, but

about a cumulative event. The interesting cognitive fact is that we do not “see” it.


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).


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 �


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 huge difference in conditional probabilities.

Many, many examples in all walks of life


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.


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)


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.


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.


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


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).

04/11/23 Round Table on ErrorsTradeoff Studies ver 4

Monty Hall Paradox*1



• 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.


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!


How much would you offer for an ice-cream cup likethe above, of your favorite flavor?

Christopher K. Hsee (University of Chicago) (1998)

Group 1


How much for this cup (again, of your favorite flavor)?

Group 2


Vendor L is more attractive for a majority of subjects tested separately.

Group 3


Hardly anyone prefers vendor L when both drawings are shown(As they are here) (Group 3)


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


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


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 all the 150 people)


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?


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.


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.


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.


A typical subjective value function: Notice the 2.5 asymmetry between gains and losses

x2.5x


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


Data fromTversky and Kahneman 1992


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”


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”


This shape reflects the all-or-none character of perceivedrisk

The weighting function becomes flatter and flatter. BUT the transitionfrom exactly zero to even very small probabilities is HUGE


As we know all too well

The total cancellation of a small risk is hugely over-rated

Even for a very, very, very small risk (one in a million)

WHILE The “mere” reduction of that same risk (from, say, ten in a million to one in a million) is vastly under-rated. Risk, in the popular mind, is something that “is

there” or “is not there” (a quantum perception) The slope of W(p) “at” zero is, in fact, infinite


Typical values

W(0.5) ~ 0.4 W(0.25) ~ 0.3 1.33 times W(0.5)/2 W(0.05) ~ 0.15 2.7 times W(0.5)/10 As probabilities decrease, the gap widens in a

spectacular way W(0.005) ~ 0.075 15 times W(0.5)/10


Some consequences Most of us are risk-averse for gains and risk-

seekers for losses We tend to evaluate gains separately from

losses We over-weigh small probabilities And under-weigh large probabilities

The dividing point is about 37% We are well calibrated around that point

Different ways of truthfully presenting the same options can have dramatic effects on decision-making and preferences

This effects are called framing effects


General culture questions

In each of the following pairs, which city has more inhabitants?

(a) Las Vegas (b) Miami

(a) Sydney (b) Melbourne

(a) Hyderabad (b) Islamabad

(a) Bonn (b) Heidelberg


How do we answer?

Recollection of facts we remember, and of scraps of information from various sources

Contingent pieces of information: This city name is quite familiar (unfamiliar) to

me My cousin visited this city It’s a capital (or is not a capital) This one has a famous University (soccer team,

arts festival, etc.), but not the other. Fame and familiarity usually go with the size of

the city.


The brute facts:

These are the real data (rounded up):

(a) Las Vegas (b) Miami 600,000 370,000 (a) Sydney (b) Melbourne 4 millions 1 million (a) Hyderabad (b) Islamabad 5.2 millions 900,000 (a) Bonn (b) Heidelberg 297,000 140,000


Over-confidence After each answer subjects are also asked: How confident are you that your answer is

correct?

50% 60% 70% 80% 90% 100% 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;

for cases in which they say that they are 90% confident, only about 70% of their answers are correct;

and for cases in which they say that they are 80% confident, only about 60% of their answers are correct.


Over-confidence This tendency toward overconfidence seems to

be very robust. 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.

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.)


Experienced horse handicappers makingpredictions on specific horses for specific races

(Paul Slovic, 1973)

Overconfidence


On overconfidence

In their domain of expertise, subjects are more accurate

But the increase in their over-confidence exceeds by far the increase in accuracy.

They are over-confident where they can do most damage


A knock-down objection, and a conclusion: Bertrand Russell, one of the greatest logicians

and philosophers of all times And a great rationalist, wrote: “It is a dangerous and self-destructive folly

to think that, since reason is not sufficient, then it is not necessary.”

In other words: We do not always have to decide rationally, in

every matter But When we intend to make a rational decision Then, it better be rational.

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

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