Local Representativeness and Distorted Bayesian Updating: A Finite-Urn Analysis

This paper develops a theoretical model of belief updating under local representativeness. Building on the finite-urn framework of Rabin (2002), we study a quasi-Bayesian agent who updates by Bayes' rule but mistakenly interprets independent and identically distributed signals as if they were drawn without replacement from a finite-urn. Under this misperception, posterior beliefs are systematically distorted, and these distortions may generate biased economic behavior. Using a beta prior, we derive closed-form results for the benchmark pure-streak case in which the perceived urn is reset every two draws. This benchmark corresponds to the canonical setting in which gambler's fallacy reasoning is typically elicited, namely prediction after a short run of identical outcomes. After two consecutive successes, the quasi-Bayesian agent becomes more willing to invest than a Bayesian, whereas after two consecutive failures, the same agent becomes more pessimistic and less willing to invest. Notably, these responses can move in the opposite direction from what a naive reading of local representativeness alone would suggest, because the effect of the finite-urn misperception on posterior beliefs is shaped by Bayesian updating and normalization. The paper also provides a behavioral characterization of the finite-urn updating rule under blockwise reset. We show how a qualitative principle of local representativeness, together with a blockwise reset assumption and a within-block predictive structure, yields the generalized finite-urn likelihood kernel used in the analysis. This characterization does not amount to a full axiomatization of dynamic choice, but it clarifies the short-run cognitive logic underlying the model. Overall, the paper offers a tractable framework for analyzing how local representativeness distorts Bayesian inference, thereby affecting posterior beliefs and economic decision-making.