Privacy, Voting, and the Wisdom of Crowds

Abstract

Companies often inform their decisions by eliciting votes from teams of internal experts (e.g., employees). However, experts might vote against their true beliefs if pressured by powerful stakeholders whose interests are misaligned with the company’s. Experts’ desire to protect their beliefs presents a privacy concern, that makes eliciting their information a challenge. This paper explores how such privacy concerns can be addressed by designing appropriate vote elicitation processes. We build a parsimonious economic model where a firm makes a binary decision based on binary votes from a team of experts. Experts observe private noisy signals about an unknown state of the world and strategically decide whether to vote truthfully. In doing so, they weigh (i) the benefit of making the firm’s decision more accurate against (ii) the privacy cost of potentially exposing their true beliefs. We show that without intervention, these privacy concerns undermine the conventional “wisdom of crowds” logic—in which having a larger pool of experts strictly improves the quality of the firm’s decisions. The optimal team size becomes finite since larger teams unravel due to free-riding by the experts. Consequently, the firm cannot always leverage the insights of all available experts. To alleviate this problem, we analyze a mechanism combining two instruments: paying accuracy bonuses and implementing randomized response (i.e., adding noise to votes). We characterize the conditions under which the optimal mechanism can restore truthful voting and enable perfect (or near-perfect) asymptotic learning. Our analytical extensions confirm the robustness of our core findings across various settings. Our numerical extensions further support the practicality of our approach, suggesting that in certain settings, even complete anonymization—a seemingly simpler and more practical option—is outperformed by the mechanisms we propose.

Keywords: differential privacy, information elicitation, privacy preservation, voting, wisdom of crowds

JEL Classification: C72, D81, D82, M20, M10