Divide or Confer: Aggregating Information without Verification

TL;DR

This paper studies how a receiver can optimally aggregate biased, unverifiable signals from many senders, revealing that in large populations, mechanisms should punish excessive consensus to improve outcomes.

Contribution

It introduces a novel large-population approach to design incentive-compatible mechanisms that account for unverifiable information and bias, extending traditional models.

Findings

Optimal mechanisms depend only on accept payoff and punish excessive consensus.

In large populations, mechanisms do not achieve first-best payoffs due to surplus burning.

Mechanisms converge to a form that balances information aggregation and bias punishment.

Abstract

We examine receiver-optimal mechanisms for aggregating information divided across many biased senders. Each sender privately observes an unconditionally independent signal about an unknown state, so no sender can verify another's report. A receiver makes a binary accept/reject decision that determines the players' payoffs via the state. When information is divided across a small population, and bias is low, the receiver-optimal mechanism coincides with the sender-preferred allocation, and can be implemented by letting senders confer privately before reporting. However, for larger populations, the receiver can benefit from the informational divide. We introduce a novel incentive-compatibility-in-the-large approach to solve the high-dimensional mechanism design problem for the large-population limit. Using this, we show that optimal mechanisms converge to one that depends only on the accept payoff and punishes excessive consensus in the direction of the common bias. These surplus burning punishments lead to payoffs that are bounded away from the first-best.