Finite languages, persuasion bias, and opinion fluctuations

We propose a boundedly rational model of opinion formation in which agents are subject to persuasion bias and communicate via finite languages. Agents are organized in a social network and repeatedly update their beliefs based on coarse messages about their neighbors' beliefs. We show that agents do not reach a consensus; instead, their beliefs keep fluctuating forever if different languages are present in their neighborhoods. In particular, we recover the classical result that under persuasion bias agents typically reach a consensus if there is a unique language in society, while small perturbations lead to fluctuations. Our approach provides and formalizes a possible mechanism to account for theories according to which storytelling may generate excessive confidence swings.