An Information Theoretic Framework For Designing Information Elicitation Mechanisms That Reward Truth-telling

TL;DR

This paper introduces an information theoretic framework called the Mutual Information Paradigm for designing mechanisms that incentivize truthful reporting in settings where information cannot be verified, overcoming key challenges like collusion and minority reporting.

Contribution

It proposes a novel mutual information-based mechanism design framework that guarantees truth-telling as a dominant strategy and unifies existing mechanisms under a common theoretical approach.

Findings

Designed mechanisms where truth-telling decreases expected payment for agents.

Unified theoretical understanding of Peer Prediction, Bayesian Truth Serum, and Dasgupta-Ghosh mechanisms.

Provided an impossibility result highlighting the framework's near-optimality.

Abstract

In the setting where information cannot be verified, we propose a simple yet powerful information theoretical framework---the Mutual Information Paradigm---for information elicitation mechanisms. Our framework pays every agent a measure of mutual information between her signal and a peer's signal. We require that the mutual information measurement has the key property that any "data processing" on the two random variables will decrease the mutual information between them. We identify such information measures that generalize Shannon mutual information. Our Mutual Information Paradigm overcomes the two main challenges in information elicitation without verification: (1) how to incentivize effort and avoid agents colluding to report random or identical responses (2) how to motivate agents who believe they are in the minority to report truthfully. Aided by the information measures we found, (1) we use the paradigm to design a family of novel mechanisms where truth-telling is a dominant strategy and any other strategy will decrease every agent's expected payment (in the multi-question, detail free, minimal setting where the number of questions is large); (2) we show the versatility of our framework by providing a unified theoretical understanding of existing mechanisms---Peer Prediction [Miller 2005], Bayesian Truth Serum [Prelec 2004], and Dasgupta and Ghosh [2013]---by mapping them into our framework such that theoretical results of those existing mechanisms can be reconstructed easily. We also give an impossibility result which illustrates, in a certain sense, the the optimality of our framework.