Keep Ballots Secret: On the Futility of Social Learning in Decision Making by Voting

TL;DR

This paper demonstrates that in team voting scenarios with Bayesian binary hypothesis testing, ignoring social learning and using secret ballots yields optimal decision-making performance, challenging common assumptions about social influence.

Contribution

The study shows that social learning is ineffective in Bayesian voting models with a fusion center, advocating for secret ballots to achieve optimal team decisions.

Findings

Social learning does not improve team decision accuracy.

Optimal performance is achieved when agents ignore precedent decisions.

Secret ballots are proven to be optimal in the model.

Abstract

We show that social learning is not useful in a model of team binary decision making by voting, where each vote carries equal weight. Specifically, we consider Bayesian binary hypothesis testing where agents have any conditionally-independent observation distribution and their local decisions are fused by any L-out-of-N fusion rule. The agents make local decisions sequentially, with each allowed to use its own private signal and all precedent local decisions. Though social learning generally occurs in that precedent local decisions affect an agent's belief, optimal team performance is obtained when all precedent local decisions are ignored. Thus, social learning is futile, and secret ballots are optimal. This contrasts with typical studies of social learning because we include a fusion center rather than concentrating on the performance of the latest-acting agents.