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Updating Beliefs When Evidence is Open to Interpretation: Implications for Bias and Polarization

48 Pages Posted: 5 Jun 2013 Last revised: 14 Mar 2017

Roland G. Fryer Jr.

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

Philipp Harms

Institute of Mathematical Stochastics

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: May 1, 2016

Abstract

We introduce a model in which agents observe signals about the state of the world, some of which are open to interpretation. Our decision makers use Bayes' rule in an iterative way: first to interpret each signal and then to form a posterior on the sequence of interpreted signals. This `double updating' leads to confirmation bias and can lead agents who observe the same information to polarize: the distance between their beliefs can grow after observing a common sequence of signals. Such updating is approximately optimal if agents must interpret ambiguous signals and sufficiently discount the future. If they are very patient but can only store interpretations of ambiguous signals, then a time-varying random interpretation rule (still double-updating) is approximately optimal. In a continuous (normally distributed) version of the model, we show that posterior beliefs never lose the influence of the prior and still always converge, but always converge to something that is influenced by the prior and early signals and so is wrong with probability one. Beliefs become arbitrarily accurate as the signal accuracy increases, but are always biased. We explore the model in an on-line experiment in which individuals interpret research summaries about climate change and the death penalty and report beliefs. Consistent with the model, not only is there a significant relationship between an individual's prior and their interpretation of the summaries; but more than half of the subjects exhibit polarizing behavior - shifting their beliefs further from the average belief after seeing the same summaries as all other subjects.

Keywords: beliefs, polarization, learning, updating, Bayesian updating, biases, discrimination, decision making

JEL Classification: D10, D80, J15, J71, I30

Suggested Citation

Fryer, Roland G. and Harms, Philipp and Jackson, Matthew O., Updating Beliefs When Evidence is Open to Interpretation: Implications for Bias and Polarization (May 1, 2016). Available at SSRN: https://ssrn.com/abstract=2263504 or http://dx.doi.org/10.2139/ssrn.2263504

Roland G. Fryer Jr.

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

American Bar Foundation

750 N. Lake Shore Drive
Chicago, IL 60611
United States

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Philipp Harms

Institute of Mathematical Stochastics ( email )

D-79104, Freiburg
Germany

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

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