Learning in a Small/Big World

TL;DR

This paper explores how the complexity of environments influences optimal learning behaviors and the extent to which humans deviate from Bayesian reasoning, especially in larger, more complex worlds.

Contribution

It models belief formation using finite automata and characterizes how optimal learning varies between small and big worlds, highlighting non-Bayesian behaviors in complex settings.

Findings

Optimal behavior aligns with Bayesian benchmarks in small worlds.

In big worlds, non-Bayesian behaviors like heuristics and over-confidence emerge.

Complexity influences the deviation from Bayesian learning.

Abstract

Complexity and limited ability have profound effect on how we learn and make decisions under uncertainty. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in small and big worlds, where the complexity of the environment is low and high, respectively, relative to the cognitive ability of the decision maker. Optimal behavior is well approximated by the Bayesian benchmark in very small world but is more different as the world gets bigger. In addition, in big worlds, the optimal learning behavior could exhibit a wide range of well-documented non-Bayesian learning behavior, including the use of heuristics, correlation neglect, persistent over-confidence, inattentive learning, and other behaviors of model simplification or misspecification. These results establish a clear and testable relationship among the prominence of non-Bayesian learning behavior, complexity, and cognitive ability.