Making Consensus Tractable

TL;DR

This paper presents an efficient algorithm for Bayesian consensus decision-making among groups, demonstrating that consensus is always achieved and the probability of error decreases exponentially with group size.

Contribution

It introduces a tractable computational method for Bayesian consensus, ensuring consensus and exponential decay of error probability in group decision-making.

Findings

Consensus is always reached in the model.

The probability of incorrect consensus decays exponentially with group size.

An efficient algorithm for the Bayesian update process is provided.

Abstract

We study a model of consensus decision making, in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current belief, and observes the votes of the rest. We provide an efficient algorithm for the calculation the agents have to perform, and show that consensus is always reached and that the probability of reaching a wrong decision decays exponentially with the number of agents.