Bayesian updating and cognitive heuristics
Marie-Pierre Dargnies
January 7, 2015
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The famous Linda problem (Tversky and Kahneman 1983)
"Linda is 31 years 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
anti-nuclear demonstrations."
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The famous Linda problem (2)
Please rank the following statements by their probability of being
true:
(1) Linda is a teacher in elementary school.
(2) Linda works in a book-store and takes Yoga-classes.
(3) Linda is active in the feminist movement.
(4) Linda is a psychiatric social worker.
(5) Linda is a member of the League of Women Voters.
(6) Linda is a bank teller.
(7) Linda is an insurance salesperson.
(8) Linda is a bank teller and is active in the feminist
movement.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The famous Linda problem (3)
Do you think (8) is more likely than (6)?
About 90% of subjects do. In a sample of well-trained
Stanford decision-sciences doctoral students, 85% do.
conjunction fallacy
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Tversky and Kahneman 1972
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:
(a) 85% of the cabs in the city are Green and 15% are Blue.
(b) A witness said the cab was Blue.
(c) The court tested the reliability of the witness during the
night and found that the witness correctly identied each of
the 2 colors 80% of the time and failed to do so 20% of the
time.
What is the probability that the cab involved in the accident is
Blue rather than Green?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Tversky and Kahneman 1972 (2)
The median and modal response in experiments is 80%.
True answer:
15%∗80%
Pr (Blue/identied as blue) = 15%∗80
%+85%∗20% = 41%
Base rate neglect
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Representativeness
What the two examples have in common: Representativeness
Representativeness can be dened as "the degree to which [an
event] (i) is similar in essential characteristics to its parent
population and (ii) reects the salient features of the process
by which it is generated" (Kahneman & Tversky, 1982).
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Representativeness and nance
Cooper et al (2001): average abnormal returns of 53 percent
associated with adding a dot-com sux to rm names during
the internet bubble (1998-1999)
independent to the extent to which the rm was actually
involved with the internet
Investors seemed to view all such rms as representative of
dot-com stocks
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Consequences of representativeness for nance
If a sector of the market is doing well, then investors may begin
to judge past performance as being representative of future
performance. It also explains why individual investors gravitate
towards the best performing mutual funds, even though past
performance is NOT representative of future results.
Representativeness causes us to underestimate the probability
of a change in the underlying trend
A number of studies indicate that extreme past winners (which
continue to win because of representativeness) become
signicant underperformers
Likewise, extreme losers tend to outperform in the years
following such poor performance.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Conservatism
2 urns, A and B, look identical from outside.
A contains 7 red and 3 blue balls.
B contains 3 red and 7 blue balls.
One urn is randomly chosen, both are equally likely.
Suppose that random draws from this urn amount to 8 reds
and 4 blues.
What is Prob(A / 8 reds and 4 blues)?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Conservatism (2)
Typical reply is between 0.7 and 0.8
But Prob(A / 8 reds and 4 blues)=0.97
Consequences: Conservatism bias implies investor
underreaction to new information
Conservatism bias can generate:
short-term momentum (tendency for rising asset prices to rise
further, and falling prices to keep falling) in stock returns
post-earnings announcement drift, i.e., the tendency of stock
prices to drift in the direction of earnings news for
three-to-twelve months following an earnings announcement
(while the information content should be quickly digested by
investors and incorporated into the ecient market price)
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Conrmatory bias (Wason 1968)
You are presented with four cards, labelled E, K, 4 and 7.
Every card has a letter on one side and a number on the other
side.
Hypothesis: "Every card with a vowel on one side has an even
number on the other side." Which card(s) do you have to turn
in order to test whether this hypothesis is always true?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Conrmatory bias (2)
Right answer: E and 7
People rarely think of turning 7.
Turning E can yield both supportive and contradicting
evidence. Turning 7 can never yield supportive evidence, but it
can yield contradicting evidence.
People tend to avoid pure falsication tests.
Conrmatory bias (too little learning)
Can lead to overcondence: investors will ignore evidence that
their strategies will lose money (Pompian 2006, Zweig 2009)
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Illusion of control
People behave as if they think they have greater control when
they roll dice themselves than when someone else rolls for
them (e.g., Fleming & Darley, 1986).
People prefer to pick their own lottery numbers than to have
others pick for them (Dunn & Wilson, 1990; Langer, 1975).
Pedestrians in New York push the walk button even though it
will not get them across the street any faster.
Illusion of control: greater condence in one's predictive ability
or in a favorable outcome when one has a higher degree of
personal involvement
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Reaction ro randomness
Imagine that you see me ipping a coin, and the outcome is:
(Head, Head, Head)
Do you believe that it is a fair coin?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Reaction ro randomness (2)
Consider sequences 1 and 2 of roulette-wheel outcomes. Is
sequence 1 less, more or equally likely?
Sequence 1: Red-red-red-red-red-red
Sequence 2: Red-red-black-red-black-black
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Reaction ro randomness (2)
Consider sequences 1 and 2 of roulette-wheel outcomes. Is
sequence 1 less, more or equally likely?
Sequence 1: Red-red-red-red-red-red
Sequence 2: Red-red-black-red-black-black
They are equally likely, but most think, that sequence 1 is less
likely.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Reaction ro randomness (3)
You ip a coin and observe Head-Head. You know that the
coin is fair.
What do you bet on for the next coin-ip, Head or Tail? Why?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Reaction ro randomness (3)
You ip a coin and observe Head-Head. You know that the
coin is fair.
What do you bet on for the next coin-ip, Head or Tail? Why?
You should be indierent.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Gambler's fallacy
Examples:
Last week's winning numbers were 2, 10, 1 and 5. Gamblers of
the current week avoid betting on these numbers.
After Head appeared twice in a fair coin-ip, most people who
know that the coin is fair would now bet on Tail.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Gambler's fallacy (2)
But:
In reality, this week it is as likely (or unlikely) as last week that
the number 2 (or 10 or 1 or 5) wins.
And "Head" is as likely to appear after "Head head" than
"Tail Tail".
Reason: The events in question are independently distributed.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Hot hand (Gilovich et al., 1985)
Most people agree with the following statements:
"A basket-ball player that scored already three times has a
higher probability of scoring with his fourth attempt than a
player that failed to score already three times."
"One should always pass the ball to a teamplayer who just
scored several times in a row."
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Hot hand (2)
But:
The data show that the scores of basket-ball players are
uncorrelated. The probability to score after three scores is not
higher than the probability to score after three failed attempts.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Gambler's fallacy and hot hand
"Gambler's Fallacy" and "Hot Hand" seem to contradict each
other.
In the rst case (GF), a sequence (...,x,x,x) inspires the belief
that the next event is likely not to be x.
In the second case (HH), people expect the exact opposite.
How can we reconcile these two biases?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Consequences: Momentum and mean reversion
"Gambler's Fallacy" => mean reversion: trends suddenly stop
working
"Hot Hand"=> momentum: a stock which has moved in one
direction is likely to continue moving in the same direction
Both eects are seen frequently in markets and there seems to
be genuine evidence for them over dierent time frames
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Law of small numbers
People tend to believe that each segment of a random
sequence must exhibit the true relative frequencies of the
events in question.
If they see a pattern of repetitions of events, i.e. a segment
that violates this "law", they believe that the sequence is not
randomly generated.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Law of small numbers (2)
In reality, representativeness of random sequences holds true
only for innite sequences.
The shorter the sequence, the less must it represent the true
frequencies of events inherent in the random process by which
it has been generated.
An innite sequence of coin-ips must exhibit 50% Heads and
50% Tails. But this is not true for nite sequences.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Law of small numbers (3)
Is this all?
Would you believe that the following sequence is random?
Head, Tail, Head, Tail, Head, Tail...
People think that repetitive patterns are not random, even if
they are. People think that randomness produces absence of
repetitive patterns.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The law of small numbers on markets
Camerer (1989): Does the Basketball Market Believe in the
"Hot Hand"? AER 79, 5, 1257- 1261.
Using a data set containing information about bets on
professional basketball games between 1983 and 1986,
Camerer nds that a small Hot-Hand-eect exists on the
betting market.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Heuristics in dealing with probabilities
Question: Is there a theory about how people who are not
rational in the sense of being Bayesian deal with probabilities?
People employ heuristics (Kahneman and Tversky)
Heuristic: mental short cuts to ease the cognitive load of
making a decision
Availability
Representativeness
Anchoring
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The availability heuristic
Used when people estimate the probability of a given event of
type T according to the number of type-T events they can
recollect.
Example: people overestimate the frequency of rare risks
(much publicity) but underestimate the frequency of common
ones (no publicity).
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
The availability heuristic (2)
Normally, one can remember the more type-T events, the more
frequently type-T events occur.
But: The ease with which we remember certain events is
inuenced by other factors, too, e.g. by the emotional content
or salience.
Since people do not correct for these other factors, the
availability heuristic is biased. (Biased sampling)
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Anchoring
Can be used whenever people start with an initial value that
they update in order to reach a nal value.
If the nal value is biased into the direction of the initial value,
this is called "anchoring" according to Kahneman & Tversky.
Example: A person stops too early to collect (costless)
information. Closely related to conservatism.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Anchoring
If traders anchor to an entry point after entering a position,
could explain why many traders will refuse to take a loss and
wait instead for the market to return to that entry point.
Salience plays an important role in anchoring: we are most
likely to anchor decisions to criteria that capture our attention.
For that reason, traders commonly anchor to high points and
low points in market movements
A useful behavioral rule is to assume that markets, in probing
to establish value, will gravitate toward the price points of
highest salience: those anchored by the largest numbers of
traders (Brett Steenbarger)
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Wishful thinking: Mayraz
Wishful thinking: the formation of beliefs and making
decisions according to what might be pleasing to imagine
instead of by appealing to evidence, rationality, or reality
Mayraz (2012): Subjects presented with a graph such as this
one:
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Wishful thinking: Mayraz (2)
Task: predict the day 100 price
Accuracy bonus for good predictions.
Farmers: gain if day 100 price is high.
Bakers: gain if day 100 price is low.
1 pound for a good prediction.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Wishful thinking: Test statistic
Treatment eect: mean prediction by farmers - mean
prediction by bakers
Null: Treatment eect ≤ 0
Wishful thinking: treatment eect>0
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Wishful thinking: Results
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Wishful thinking: conclusion
Bias independent of incentives for accuracy, increases with
uncertainty, appears to be increasing with what's at stake.
We should expect bias whenever decisions are based on
subjective judgment, including environments in which biased
beliefs have costly consequences.
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics
Monty Hall Problem
Named after a 1970s US game show called "Let's Make a
Deal" that was hosted by Monty Hall.
A contestant is shown 3 closed doors. Behind one is a desirable
and high-value grand prize such as a car or a motorboat.
The remaining two doors conceal a fake prize: a goat.
The contestant is invited to choose one of the doors to be
opened
Let's say the contestant chooses door a.
Now Monty Hall reveals a goat behind one of the remaining 2
doors: let's say it's door b.
Does the contestant want to switch to door c or stay with his
original choice of a?
What would you do?
Marie-Pierre Dargnies
Bayesian updating and cognitive heuristics