Friday, 15 November 2013

Heuristics and Errors in Probability Estimation

Heuristics and Errors in Probability Estimation (Reference: Wilkinson and Klaes, An Introduction to Behavioral Economics, Page 117-124, Palgrave Macmillan, 2nd Edition, 2012.)
 Teaching note By Munish Alagh.
In the standard model of microeconomics we examine how people form attitudes, values, preferences and finally make choices. Various assumptions are made regarding the options and outcomes of these options in the decision making process. As far as beliefs are concerned, a main assumptions in the standard model is that they are Bayesian Probability Estimators.
Bayesian Probability Estimators: This means that people are able to estimate probabilities correctly, given the relevant information, and in particular are able to update them correctly given a sequence of prior outcomes
Specifically, Bayes Theorem updates or modifies probabilitys, given new pieces of evidence ( Refer to Wilkinson and Klaes for full mathematical statement of the theorem.)
Probability Estimation
The types of deviation described in this section refer to rational Bayesian updating.
The availability heuristic:salience, or people believe events are more probable if examples are more easy to remember.
Representativeness heuristic:
People evaluate likelihood of a subject belonging to a particular category, based on the degree to which the subject resembles a typical item in that category.For eg (Refer Wilkinson and Klaes for ‘Linda is a Bank Teller” example where strong representativeness overcomes the feature thatProbability of two events can never be higher than a single one.)
Base Rate Bias-People tend to ignore the base rate, for eg: however high the odds and despite error being 95%, a positive result of a test is taken as a confirmation of disease.
The law of small numbers: principles that apply to infinite populations are assumed to apply to small samples.
Gamblers fallacy: gamblers frequently expect a certain slot machine or a number that has not won in a while to be ‘due” to win: Caused due to Misapplication of the assumption of non-replacement.
Hot hand effect: The effect derives its name from the mistaken belief among basketball players that a players chance of hitting a shot is greater following a hit than following a miss on the previous shot. Although it appears that  this “overinference” is the opposite of the gamblers fallacy, it is actually a complementary effect, again involving a misapplication of the assumption of non-replacement.
Synthesis: The law of small numbers could lead to both hot hand and gamblers fallacy, causing both underreaction and over reaction to market signals, in the short term investors follow the gamblers fallacy, however after a longer sequence, investors overinfer.

In terms of a lottery situation, the law of small numbers could lead to people exhibiting a gamblers fallacy and expecting winning numbers to not repeat, however with regard to stores there may be a human element with regard to how stores are selected leading to a hot hand.

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