09. Representativeness Flashcards
What are heuristics?
A heuristic is a rule of thumb: often rules of thumb can be quite accurate under some circumstances.
Other times, heurstics are systematically flawed and lead to biased decisions.
What is the conjunction fallacy?
P(B and F) > P(B) is a violation of the conjunction fallacy.
Finding replicated with many different groups.
Naive subjects: undergraduates with no statistical knowledge.
Intermediate and sophisticated subjects: with some/a lot of statistical knowledge.
If we judge the likelihood of an event using the representativeness heurstic, we are likely to make mistakes.
What is base rate neglect?
When asked about the likelihood that Linda is of a certain type (F) given an description of Linda (D), we seem to evaluate P(F/D) = P(D/F)
P(D/F) provides a measure for how representative Linda’s description is of a specific type F.
According to Bayes rule we should also take P(F) into account: the base rate.
Bayes rule: consider 2 events D and F: P(F/D) = P(D/F)*P(F)/P(D)
By using the representativeness heuristic people seem to neglect the information contained in P(F) = base rate neglect. Representativeness violates the Bayes rule.
The bias arises when we judge without prior probabilities.
What is the taxicab problem?
A cab was involved in a hit and run accident at night.
2 companies the Green and Blue: 85% of the cabs in the city are Green and 15% are Blue.
A witness identified as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the 2 colors 80% of the time and failed 20% of the time.
Whats the probability that the cab involved in the accident was Blue rather than Green?
What is misconception of chance?
People expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short.
Eg. Peole regard the sequence HTHTTH to be more likely than the sequence HHHTTT, which does not appear to be random.
What is the law of small numbers?
Misconception of chance is also the law of small numbers.
Law of large numbers: large random sample from a population will have a distribution that closely resembles that of the overall population.
Law of small numbers: exaggeration of likelihood that a small sample resembles the parent population from which it is drawn.
Rabin (2002) belief in the law of small numbers can give rise to gambler’s and hot-hand fallacy.
What did Rabin (2002) examine?
A person observes a sequence of binary singles (A,b) of some quality.
Eg. A sequence of good or bad investments by a mutual-fund manager that signals competence, or performances by a company that signals its long-run prospects.
Whereas in reality these signals are generated by an i.i.d process = likelihood of signal a is theta and likelihood of b is (1-theta), the person believes that they are generated by random draws without replacecement from an urn of size N.
Without replacement captures belif in the law of small numbers = means that the observer believes that the proportion of signals must balance out to the popluation rate before N signals are observed.
Rabin (2002) shows: as N becomes infinitely large, the person becomes fully Bayesian, the smaler is N, the more he believes in the law of small numbers.
This model can explain: gambler’s and hot-hand fallacy.
What is the gambler’s fallacy?
The belief that if deviations from expected behaviour are observed in repeated trials of some random process, then these deviations are likely to be evened out by opposite deviations in the future.
Rabin (2002): people except the second draw of a signal to be negatively correlated with the first draw.
If an investor believes that particular fund manager invests succesfully close to half the time even over short intervals, then he thinks that the success in one year implies less than 1/2 chance of success in the following year.
What if we do not know the odds?
So far only with known probabilities.
If odds are not known, representativeness-based thinking leads a person to try to uncover the process through observation. The person begins to ask: for what process is the observed sequence representative?
What is the hot-hand fallacy?
In cases where the data-generating process is unknown, people tend to infer it too quickly on the basis of too few data points.
Exaggerating the likelihood that a short sequence of signals will closely resemble the underlying rate leads to exaggerating the likelihood that the underlying rate resembles a short sequence of signals.
Eg. If a person believes every pair of flips of a fair coin generates one head and one tail, then he believes that two heads in a row indicate a biased coin.
What is the Rabin-type beliefs?
The Rabin-type assigns a lower probability to a streak of two a’s than a Bayesian, because he believes that no matter the rate, drawing the first a means that there are fewer a’s left for the second draw.
Rabin Type’s beliefs are too skewed toward believing that the fund is good, since making one less a available for the second draw has a proportionally greater impact when there are fewer a’s to begin with.
From his priors, the Rabin-type forms probabilistic beliefs about the rate given an observed sequence of signals.
Bayesian believes that the analyst is good 18/28, Rabin-type: 21/28
What did De Bondt (1993) study?
De Bondt (1993) studied the prediction of speculative price series which differ in their apparent past trends. 38 000 forecasts are examined.
2 major results:
1) Many individuals predict asset prices by extrapolating from past trends = related to hot-hand
2) Subjects exhibit caution in their projections of the range of future prices
Experts seem to judge differently.
They are contrarians and believe in mean-reversion = related to Gamblers
The experts had more information about the market conditions when they made their forecast.
What is the illusion of validity?
People often judge by selecting the outcome (eg. Occupation) that is most representative of the input (eg. Description)
It has also been found that the confidence they have in the judgement depends primarily on the representativeness of the information… with little regard for factors that limit its accuracy.
What is representativeness?
A person who relies on representativeness “evaluates the probibility of an unvertain event by the degree to which sample evidence is
(1) Similar in essential proprteis to its parent population
(2) Reflects the salient features of the process by which it is generated”.
