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

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 high-quality reports 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 pays better than any other strategy profile (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—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 that illustrates, in a certain sense, the the optimality of our framework.