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On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity

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Abstract

The Condorcet efficiency of a social choice procedure is usually defined as the probability that this procedure coincides with the majority winner (or majority ordering) in random samples, given a majority winner exists (or given the majority ordering is transitive). Consequently, it is in effect a conditional probability that two sample statistics coincide, given certain side conditions. We raise a different issue of Condorcet efficiencies: What is the probability that a social choice procedure applied to a sample matches with the majority preferences of the population from which the sample was drawn? We investigate the canonical case where the sample statistic is itself also majority rule and the samples are drawn from real world distributions gathered from national election surveys in Germany, France, and the United States. We relate the results to the existing literature on majority cycles and social homogeneity. We find that these samples rarely display majority cycles, whereas the probability that a sample misrepresents the majority preferences of the underlying population varies dramatically and always exceeds the probability that the sample displays cyclic majority preferences. Social homogeneity plays a fundamental role in the type of Condorcet efficiency investigated here.

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Authors and Affiliations

  1. Department of Psychology, Quantitative Division, University of Illinois at Urbana-Champaign, Champaign, IL, 61820

    Michel Regenwetter (Assistant Professor of Psychology)

  2. Department of Political Science, University of California at Santa Barbara, Santa Barbara, CA, 93106

    James Adams (Associate Professor of Political Science)

  3. School of Social Sciences, University of California at Irvine, Irvine, CA, 92697-5100

    Bernard Grofman (Professor of Political Science)

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  1. Michel Regenwetter
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  2. James Adams
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  3. Bernard Grofman
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Regenwetter, M., Adams, J. & Grofman, B. On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity. Theory and Decision 53, 153–186 (2002). https://doi.org/10.1023/A:1021215903030

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