Indirect reciprocity under opinion synchronization

TL;DR

This paper presents a unified model of indirect reciprocity showing that cooperation stability hinges on opinion correlation among individuals, influenced by social norms and interaction structures.

Contribution

It introduces a framework that reconciles public and private assessment models by linking cooperation stability to opinion correlation.

Findings

Cooperation is unstable when individual opinions are independent.

Opinion correlation enhances the stability of cooperative norms.

The model explains the effects of social norms and interaction structures on cooperation.

Abstract

Indirect reciprocity is a key explanation for the exceptional magnitude of cooperation among humans. This literature suggests that a large proportion of human cooperation is driven by social norms and individuals' incentives to maintain a good reputation. This intuition has been formalized with two types of models. In public assessment models, all community members are assumed to agree on each others' reputations; in private assessment models, people may have disagreements. Both types of models aim to understand the interplay of social norms and cooperation. Yet their results can be vastly different. Public assessment models argue that cooperation can evolve easily, and that the most effective norms tend to be stern. Private assessment models often find cooperation to be unstable, and successful norms show some leniency. Here, we propose a model that can organize these differing results within a single framework. We show that the stability of cooperation depends on a single quantity: the extent to which individual opinions turn out to be correlated. This correlation is determined by a group's norms and the structure of social interactions. In particular, we prove that no cooperative norm is evolutionarily stable when individual opinions are statistically independent. These results have important implications for our understanding of cooperation, conformity, and polarization.