Elicitability and knowledge-free elicitation with peer prediction

Abstract

The elicitation of private information from individuals is crucially important to many real-world tasks. But elicitation is most challenging when it is most useful: when objective (verifiable) truth is inaccessible or unavailable, and there is no ``answer key available to verify reports. Prior work has designed mechanisms that truthfully elicit private information without verification for some restricted set of possible information structures of the participants (i.e. the common prior joint distributions of participants' signals). In fact, no mechanism can elicit private information truthfully for all information structures without verification. In this paper, we identify the maximal set of information structures that are truthfully elicitable without verification, and provide a mechanism for such elicitation. This mechanism requires that the designer know the information structure of the participants, which is unavailable in many settings. We then propose a knowledge-free peer prediction mechanism that does not require knowledge of the information structure and can truthfully elicit private information for a set of information structures slightly smaller than the maximal set. This mechanism works for both small and large populations in settings with both binary and non-binary private signals, and is effective on a strict superset of information structures as compared to prior mechanisms that satisfy these properties.