An axiomatic approach to the law of small numbers
Noor, Jawwad (Boston University)
Payro Chew, Fernando (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)

Imprint:	Barcelona Barcelona School of Economics, 2022
Description:	25 pàg.
Abstract:	With beliefs over the outcomes of coin-tosses as our primitive, we formalize the Law of Small Numbers (Tversky and Kahneman (1974)) by an axiom that expresses a belief that the sample mean of any sequence will tend towards the coin's perceived bias along the entire path. The agent is represented by a belief that the bias of the coin is path-dependent and self-correcting. The model is consistent with the evidence used to support the Law of Small Numbers, such as the Gambler's Fallacy. In the setting of Bayesian inference, we show how learning is affected by the interplay between two potentially opposing forces: a belief in the absence of streaks and a belief that the sample mean will tend to the true bias. We show that, unlike other learning results in the literature (Rabin (2002), Epstein, Noor, and Sandroni (2010)), the latter force ensures that the agent at least admits the true parameter as possible in the limit, if not learn with certainty that it is true. In an evolutionary setting, we show that agents who believe in the Law of Small Numbers are never pushed out of the evolutionary race by "standard" agents who correctly understand randomness.
Grants:	Agencia Estatal de Investigación PGC2018-094348-B-I00 Agencia Estatal de Investigación CEX 2019-000915-S
Rights:	Tots els drets reservats.
Language:	Anglès
Series:	BSE working paper ; 1364
Document:	Working paper ; recerca
Subject:	Law of Small Numbers ; Belief Biases ; Heuristics ; Gambler's Fallacy ; Learning ; Misspecified beliefs ; Evolution
Published in:	BSE Barcelona School of Economics Working Papers, 2022

Adreça alternativa: https://bse.eu/research/working-papers/axiomatic-approach-law-small-numbers

26 p, 667.9 KB

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