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Scoring from Contests

Published online by Cambridge University Press:  04 January 2017

Keith E. Schnakenberg*
Department of Political Science, Washington University in St. Louis, 1 Brookings Drive, Campus Box 1063, St. Louis, MO 63105
Elizabeth Maggie Penn
Department of Political Science, Washington University in St. Louis e-mail:
e-mail: (corresponding author)


This article presents a new model for scoring alternatives from “contest” outcomes. The model is a generalization of the method of paired comparison to accommodate comparisons between arbitrarily sized sets of alternatives in which outcomes are any division of a fixed prize. Our approach is also applicable to contests between varying quantities of alternatives. We prove that under a reasonable condition on the comparability of alternatives, there exists a unique collection of scores that produces accurate estimates of the overall performance of each alternative and satisfies a well-known axiom regarding choice probabilities. We apply the method to several problems in which varying choice sets and continuous outcomes may create problems for standard scoring methods. These problems include measuring centrality in network data and the scoring of political candidates via a “feeling thermometer.” In the latter case, we also use the method to uncover and solve a potential difficulty with common methods of rescaling thermometer data to account for issues of interpersonal comparability.

Research Article
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Authors' note: We are grateful for the helpful comments of David Darmofal, Mark Fey, Holger Kern, John Patty, and especially Stephane Wolton, along with seminar participants at Washington University, the Harris School of Public Policy, the University of South Carolina, the Stanford Graduate School of Business, the University of Maryland, and the University of Pittsburgh. This research was supported by NIH Grant (#1RC4LM010958-01), and we are particularly indebted to William Shannon, Elena Deych, Skye Buckner-Petty, and Berkley Shands at the Washington University School of Medicine for their support. Replication materials for this article are available from the Political Analysis Dataverse at


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