Rational Social Learning by Random Sampling

22 Pages Posted: 28 May 2008 Last revised: 9 Jul 2013

See all articles by Lones Smith

Lones Smith

University of Wisconsin at Madison - Department of Economics

Peter Norman Sorensen

University of Copenhagen - Department of Economics

Date Written: July 7, 2013

Abstract

This paper explores rational social learning in which everyone only sees unordered random samples from the action history. In this model, herds need not occur when the distant past can be sampled. If private signal strengths are unbounded and the past is not over-sampled -- not forever affected by any individual -- there is complete learning and a correct proportionate herd. With recursive sampling, welfare almost surely converges under the new proviso that the recent past is not over-sampled. In this case, there is almost surely complete learning with unbounded beliefs and unit sample sizes. The sampling noise in this Polya urn model induces a path-dependent structure, so that re-running the model with identical signals generally produces different outcomes.

Keywords: herding, cascades, Polya urns, martingales

JEL Classification: D8

Suggested Citation

Smith, Lones and Sorensen, Peter Norman, Rational Social Learning by Random Sampling (July 7, 2013). Available at SSRN: https://ssrn.com/abstract=1138095 or http://dx.doi.org/10.2139/ssrn.1138095

Lones Smith (Contact Author)

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

Peter Norman Sorensen

University of Copenhagen - Department of Economics ( email )

Oster Farimagsgade 5
Building 26
Copenhagen K, 1353
Denmark
+45 35 32 3056 (Phone)

HOME PAGE: http://www.econ.ku.dk/sorensen

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