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False Consensus, Information Theory, and Prediction Markets

Authors Yuqing Kong , Grant Schoenebeck

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Author Details

Yuqing Kong
  • The Center on Frontiers of Computing Studies, School of Computer Science, Peking University, China
Grant Schoenebeck
  • School of Information, University of Michigan, Ann Arbor, MI, USA

Funding

  • Kong, Yuqing: This work is supported by National Natural Science Foundation of China award number 62002001.
  • Schoenebeck, Grant: This work is supported by NSF CAREER 1452915 and NSF CCF 2007256.

Cite As Get BibTex

Yuqing Kong and Grant Schoenebeck. False Consensus, Information Theory, and Prediction Markets. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 81:1-81:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ITCS.2023.81

Abstract

We study a setting where Bayesian agents with a common prior have private information related to an event’s outcome and sequentially make public announcements relating to their information. Our main result shows that when agents' private information is independent conditioning on the event’s outcome whenever agents have similar beliefs about the outcome, their information is aggregated. That is, there is no false consensus. 
Our main result has a short proof based on a natural information-theoretic framework. A key ingredient of the framework is the equivalence between the sign of the "interaction information" and a super/sub-additive property of the value of people’s information. This provides an intuitive interpretation and an interesting application of the interaction information, which measures the amount of information shared by three random variables. 
We illustrate the power of this information-theoretic framework by reproving two additional results within it: 1) that agents quickly agree when announcing (summaries of) beliefs in round-robin fashion [Aaronson 2005], and 2) results from [Chen et al 2010] on when prediction market agents should release information to maximize their payment. We also interpret the information-theoretic framework and the above results in prediction markets by proving that the expected reward of revealing information is the conditional mutual information of the information revealed.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • Agreeing to disagree
  • false consensus
  • information theory
  • prediction market

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