Incentive-Compatible Inference from Subjective Opinions Without Common Belief Systems

Abstract Peer-prediction mechanisms elicit information about unverifiable or subjective states of the world. Existing mechanisms in the class are designed so participants maximize their expected payments when reporting honestly. However, these mechanisms do not account for participants desiring influence over how reports are used. When participants want the conclusions drawn from reports to reflect their own opinion, the inference procedure must be subjected to incentive-compatibility constraints to ensure honesty. In this paper, I develop mechanisms without payments for discerning the true answer to a binary question, even in the presence of a false consensus. I first characterize all continuous, neutral, and anonymous mechanisms in this setting that can be implemented in interim-rationalizable strategies. Using this representation, I optimize across the class of mechanisms for accuracy in distinguishing the true state. Because the mechanism does not require knowledge of the distribution of agent types and is neutral between both outcomes, it can serve as a test for bias in the surveyed population