Emergence of Collective Accuracy in Socially Connected Networks

TL;DR

This paper demonstrates that in large social networks, collective decision accuracy can surpass individual accuracy due to local interactions and social influence, especially when private signals are slightly biased towards the correct choice.

Contribution

It analytically characterizes how social influence in networks enhances collective accuracy beyond individual capabilities in large populations.

Findings

Collective accuracy converges to a nontrivial limit involving the incomplete beta function.

Network influence can improve group decision accuracy when private signals are biased.

The results inform design of resilient decision-making in social and engineered networks.

Abstract

We analyze the accuracy of collective decision-making in socially connected populations, where agents update binary choices through local interactions on a network. Each agent receives a private signal that is biased -- even marginally -- toward the correct alternative, and social influence mediates the aggregation of these signals. We show analytically that, in the large-population limit, the probability of a correct majority converges to a nontrivial expression involving the regularized incomplete beta function. Remarkably, this collective accuracy surpasses that of any individual agent whenever private signals are better than random, revealing that network-mediated influence can enhance, rather than impair, group performance. Our findings may inform the design of resilient decision-making systems in social, biological, and engineered networks, where accuracy must emerge from interdependent and noisy agents.