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Scoring from Contests

  • Keith E. Schnakenberg (a1) and Elizabeth Maggie Penn (a2)
Abstract

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.

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e-mail: keschnak@wustl.edu (corresponding author)
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John Aitchison . 1986. The statistical analysis of compositional data. Monographs on Statistics and Applied Probability. London: Chapman & Hall.

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John W. Patty , Elizabeth M. Penn , and Keith E. Schnakenberg 2013. Measuring the latent quality of precedent: Scoring vertices in a network. In Advances in political economy: Institutions, modelling and empirical analysis, eds. Daniel Kselman , Gonzalo Caballero , and Norman Schofield . Berlin: Springer.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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