Emergence of Collective Accuracy in Socially Connected Networks

TL;DR

This study addresses how collective decision-making in socially connected populations can surpass individual accuracy when private signals are slightly biased toward the correct choice. It analyzes a voter-model-like process on a network with $\\alpha$ fixed voters in the correct state and $\\beta$ fixed voters in the incorrect state, proving that in the large-population limit the fraction of correct free voters converges to a $V\\sim \\text{Beta}(\\alpha,\\beta)$ distribution, with the probability of a correct majority given by $P(V\\ge 1/2)=1-I_{1/2}(\\alpha,\\beta)$. A key contribution is showing that for $\\alpha>\\beta$, this collective probability exceeds the per-voter accuracy $p=\\alpha/(\\alpha+\\beta)$, i.e., social influence amplifies private information through the Beta-distributed limit. The work thus provides a bridge between Condorcet-style jury theory and beta-distribution limits, with implications for designing resilient decentralized decision-making in social, biological, 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.