Updating Beliefs with Ambiguous Evidence: Implications for Polarization

23 Pages Posted: 8 Jun 2013

See all articles by Roland G. Fryer

Roland G. Fryer

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); American Bar Foundation; University of Chicago

Philipp Harms

University of Freiburg - Institut für Mathematische Stochastik

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)

Multiple version iconThere are 2 versions of this paper

Date Written: June 2013

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.

Suggested Citation

Fryer, Roland G. and Harms, Philipp and Jackson, Matthew O., Updating Beliefs with Ambiguous Evidence: Implications for Polarization (June 2013). NBER Working Paper No. w19114. Available at SSRN: https://ssrn.com/abstract=2276376

Roland G. Fryer (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
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National Bureau of Economic Research (NBER)

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American Bar Foundation

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University of Chicago ( email )

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Philipp Harms

University of Freiburg - Institut für Mathematische Stochastik ( email )

Freiburg, 79104
Germany

Matthew O. Jackson

Stanford University - Department of Economics ( email )

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Stanford, CA 94305-6072
United States
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HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

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United States

Canadian Institute for Advanced Research (CIFAR) ( email )

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Toronto, Ontario
Canada

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