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Experimental and Behavioral Economics

Lecture 2: Bayesian updating and

cognitive heuristics

Prof. Dr. Dorothea Kübler Summer term 2019

1

Memos Thank you for sending them! Many good summaries, some very very short…but I accepted all of them unless you received an email from me. A criticism voiced by one of you: early experiments were designed to support the theory, results are not surprising (e.g., regarding indifference curves). Many pointed out that early experiments laid the foundations in terms of methodology (paying subjects etc.).

The famous „Linda Problem“

(Tversky and Kahnemann 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.“

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.

Do you believe that (8) is more likely than (3)? Almost no one does. Do you believe that (8) is more likely than (6)? About 90% of subjects do. In a sample of well-

trained Stanford decison-science doctoral students, 85% do.

They all commit the conjuction fallacy. Why?

Conjunction fallacy. Conjunction law of probabilities: P(A&B)≤ P(A)

A. Linda is a bank teller (6) B. Linda is active in the feminist movement (3) A&B. Linda is a bank teller and is active in the feminist movement. (8)

From the conjunction law follows that P(8)

Another bias (Kahnemann & Tversky,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 at night and

found that the witness correctly identified each of the two 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?

What is the probability that the cab involved in the accident is Blue rather than Green? The median and modal response in experiments is 80%.

Base rate neglect Updating belief X after learning M should follow rule Bayes’ Rule:

𝑃 𝑋 𝑀 = 𝑃 𝑀 𝑋 𝑃(𝑋) 𝑃(𝑀)

X- Car was Blue M- Witness identifies the car as blue

𝑃 𝐵𝐵𝐵𝐵 𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵 = 𝑃 𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 ∙ 𝑃(𝐵𝐵𝐵𝐵)

𝑃(𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵)

= 𝑃 𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 ∙ 𝑃(𝐵𝐵𝐵𝐵)

𝑃 𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵 𝐵𝐵𝐵𝐵 ∙ 𝑃 𝐵𝐵𝐵𝐵 + 𝑃 𝐼𝐼𝐵𝐼𝐼. 𝑏𝐵𝐵𝐵 𝐼𝑛𝐼 𝑏𝐵𝐵𝐵 ∙ 𝑃 𝐼𝑛𝐼 𝑏𝐵𝐵𝐵

= 80%∙15% 80%∙15%+20%∙85%

= 41%

Given that the proportion of blue cabs in the city is only 15%, the posterior probability is not correctly updated: Base rate neglect

What do the two examples have in common?

Representativeness Representativeness can be defined as „the degree to which an event : (i) is similar in essential characteristics to its parent

population and (ii) reflects the salient features of the process by which it is

generated“ (Kahnemann& Tversky, 1982, p.33).

Another violation of Bayes’ rule (Edwards, 1968)

2 urns, A and B, look identical from outside. A: 7 red and 3 blue balls. B: 3 red and 7 blue balls. One urn is randomly chosen, both are equally likely. Suppose that random draws with replacement from

this urn amount to 8 reds and 4 blues. What is the probability that the urn is A?

Typical reply is between 0.7 and 0.8 But Prob(A I 8 reds and 4 blues)=0.967

Conservatism - underweighting of likelihood information.

Conservatism versus base rate neglect:

contradiction? Griffin and Tversky (1992): people overweight the

strength of evidence and underemphasize its weight

Obstacles to learn: two more biases 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?

Right answer: E and 7 Why 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.

Confirmatory Bias:

People tend to avoid pure falsification tests. Too little learning.

Self-fulfilling prophecies If people believe a hypothesis is true, their actions often produce a biased sample of evidence that reinforces their belief. Example: If waiter has stereotype that young patrons do not tip well (she may display confirmation bias by remembering times that young patrons have not tipped well and ignoring times when young patrons have tipped well), this stereotype may become a self-fulfilling prophecy in that she may talk differently and wait less on young patrons, which in turn may make them tip less (thereby confirming the stereotype). Thus both confirmation bias and self-fullfilling prophecies inhibit learning.

Monty Hall problem.

One door has a car behind it, and behind other doors is a goat. Which door do you choose?

Would you like to change you choice?

Monty Hall problem Most people stick to the original choice, but this violates Bayes’ Rule. 𝑃 𝑋 𝑀 = 𝑃 𝑀 𝑋 𝑃(𝑋)

𝑃(𝑀)

𝑃 𝐶𝐶𝐶1 𝑛𝑜𝐵𝐼𝑜, 𝑐𝑐𝑛𝑐𝐵1 = 𝑃 𝑛𝑜𝐵𝐼𝑜 𝑐𝐶𝐶1, 𝑐𝑐𝑛𝑐𝐵1 𝑃(𝑐𝐶𝐶|𝑐𝑐𝑛𝑐𝐵1)

𝑃(𝑛𝑜𝐵𝐼𝑜|𝑐𝑐𝑛𝑐𝐵1) = 0.5 ∙ 1𝑜

0.5 = 1 𝑜

𝑃 𝐶𝐶𝐶𝐶 𝑛𝑜𝐵𝐼𝑜, 𝑐𝑐𝑛𝑐𝐵1 = 𝑃 𝑛𝑜𝐵𝐼𝑜 𝑐𝐶𝐶𝐶, 𝑐𝑐𝑛𝑐𝐵1 𝑃(𝑐𝐶𝐶|𝑐𝑐𝑛𝑐𝐵1)

𝑃(𝑛𝑜𝐵𝐼𝑜|𝑐𝑐𝑛𝑐𝐵1) = 1 ∙ 1𝑜 0.5 =

𝐶 𝑜

Monty Hall problem in markets Kluger and Wyatt (2004) Two types of assets in the experiment: With and without the right to „switch doors“ Prediction: The asset’s price with right should be twice as high as asset’s price without the right. Market aggregation („market magic“): if at least two out of six participants are rational Bayesians, the prices should be close to fundamental value. Result: Only 25% of groups were close to rational prices.

Randomness Is randomness intuitive? Consider sequence 1 and 2 of roulette-wheel outcomes. Sequence 1: Red-red-red-red-red-red Sequence 2: Red-red-black-red-black-black Is sequence 1 less, more or equally likely? They are equally likely, but most think that sequence 1 is less likely.

Representativeness/ Law of Small Numbers 1. Representiveness does not respect sample size

2. Law of small numbers (Tversky and Kahnemann 1971):

„All samples will closely resemble the process or populations that

generated them“ 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. „Hot hand“ for example.

Only law of large numbers is true In reality, representativeness of random sequences holds true only for infinite sequences („law of large numbers“). The shorter the sequence, the less it must represent the true frequencies of events inherent in the random process by which it has been generated. An infinite sequence of coin-flips must exhibit 50% Heads and 50% Tails. But this is not true for finite sequences.

Can people easily generate random sequences? Often people generate sequences with negative

autocorrelation (Wagenaar, 1972). Direct consequence of the

law of small numbers.

Who is doing better than average?

1. Mathematically sophisticated

2. Experienced (trained)

3. Children (Ross and Levy 1958)

Gambler’s Fallacy Another