Rabin (2007) "INFERENCE BY BELIEVERS IN THE LAW OF SMALL NUMBERS" Class 7 Flashcards
What is the law of small numbers?
When people expect a small sample to be representative of the distribution of the true population
What is the gamblers fallacy (pg 2 of paper)
They believe the 2nd outcome is negatively correlated to the 1st outcome.
E.g.
Due to the law of small numbers if they know that a fund manager has a good underlying performance, if they perform badly in one year they’ll overreact to this signal and think that in the next year it’s extremely likely they’ll perform well. Even though in the long term this manager does perform well, 2 years is not the long term.
What issues can believing in the law of small numbers bring about?
Gamblers fallacy
Over-inference
What is over-inference?
Since this person believes a small sample is representative of the distribution of the true population if they see a few signals they’ll overly make assumptions.
E.g. if they see that 2 times when a coin was tossed that it was tails they’ll believe the coin is biased
If this was gamblers fallacy they would believe that it is extremely likely that if you tossed the coin again it’d be heads.
STREAKINESS
Expect a small sample of signals of a long sequence to have same distribution as the whole sequence of signals
What does the STANDARD economic model predict?
That people will use Bayesian updating
What experiment did Rabin use to test for the law of small numbers?
Either a positive signal a or, a negative signal b can be drawn. These draws are identically independently distributed (i.i.d).
However someone who is not Bayesian will believe that each signal is taken without replacement from an urn of size N ( so each time the signal is a the probability of a being picked next time is lower than before)
He believes the urn is renewed after every 2 draws so on every odd draw he is observing a signal from a new urn and in every even draw he is observing a signal from the urn from the previous draw WITHOUT replacement.
