Technical Report No. 267 - Abstract

Jens Witkowski and David C. Parkes:
A Robust Bayesian Truth Serum for Small Populations

Peer prediction methods allow the truthful elicitation of private signals (e.g., experiences, or opinions) in regard to a true world state when this ground truth is unobservable. The original peer prediction method is incentive compatible for any finite number of agents n ≥ 2 but critically relies on a common prior, shared by all agents and the center. The Bayesian Truth Serum (BTS) relaxes this assumption. While it still assumes that the agents share a common prior, this prior need not be known by the center. However, BTS is proven to be incentive compatible only for a large enough number of agents, and this number depends on the prior and is thus unknown to the mechanism. In this paper, we present a robust BTS for the elicitation of binary information which is incentive compatible for any n ≥ 3, taking advantage of a particularity of the quadratic scoring rule. Our mechanism is the first peer prediction method that does not rely on knowledge of the common prior to provide strict incentive compatibility for any n ≥ 3. Moreover, and in contrast to the original BTS, our mechanism is numerically robust and ex post individually rational.