License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.81
URN: urn:nbn:de:0030-drops-175844
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17584/
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Kong, Yuqing ; Schoenebeck, Grant

False Consensus, Information Theory, and Prediction Markets

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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.

BibTeX - Entry

@InProceedings{kong_et_al:LIPIcs.ITCS.2023.81,
  author =	{Kong, Yuqing and Schoenebeck, Grant},
  title =	{{False Consensus, Information Theory, and Prediction Markets}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{81:1--81:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17584},
  URN =		{urn:nbn:de:0030-drops-175844},
  doi =		{10.4230/LIPIcs.ITCS.2023.81},
  annote =	{Keywords: Agreeing to disagree, false consensus, information theory, prediction market}
}

Keywords: Agreeing to disagree, false consensus, information theory, prediction market
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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