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Updating Beliefs with Ambiguous Evidence: Implications for Polarization

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  • Roland G. Fryer, Jr.
  • Philipp Harms
  • Matthew O. Jackson

Abstract

We introduce and analyze a model in which agents observe sequences of signals about the state of the world, some of which are ambiguous and open to interpretation. Instead of using Bayes' rule on the whole sequence, our decision makers use Bayes' rule in an iterative way: first to interpret each signal and then to form a posterior on the whole sequence of interpreted signals. This technique is computationally efficient, but loses some information since only the interpretation of the signals is retained and not the full signal. We show that such rules are optimal if agents sufficiently discount the future; while if they are very patient then a time-varying random interpretation rule becomes optimal. One of our main contributions is showing that the model provides a formal foundation for why agents who observe exactly the same stream of information can end up becoming increasingly polarized in their posteriors.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 19114.

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Date of creation: Jun 2013
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Handle: RePEc:nbr:nberwo:19114

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  1. Edward L. Glaeser & Cass R. Sunstein, 2013. "Why Does Balanced News Produce Unbalanced Views?," NBER Working Papers 18975, National Bureau of Economic Research, Inc.
  2. Joan Esteban & Debraj Ray, 2011. "Linking Conflict to Inequality and Polarization," American Economic Review, American Economic Association, vol. 101(4), pages 1345-74, June.
  3. Coate, S. & Loury, G.C., 1992. "Will Affirmative Action Policies Eliminate Negative Stereotypes?," Papers 3, Boston University - Department of Economics.
  4. Fryer Roland & Jackson Matthew O., 2008. "A Categorical Model of Cognition and Biased Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-44, February.
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