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On the probabilities of correct or incorrect majority preference relations

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  • Ilia Tsetlin
  • Michel Regenwetter

Abstract

While majority cycles may pose a threat to democratic decision making, actual decisions based inadvertently upon an incorrect majority preference relation may be far more expensive to society. We study majority rule both in a statistical sampling and a Bayesian inference framework. Based on any given paired comparison probabilities or ranking probabilities in a population (i.e., culture) of reference, we derive upper and lower bounds on the probability of a correct or incorrect majority social welfare relation in a random sample (with replacement). We also present upper and lower bounds on the probabilities of majority preference relations in the population given a sample, using Bayesian updating. These bounds permit to map quite precisely the entire picture of possible majority preference relations as well as their probabilities. We illustrate our results using survey data. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Ilia Tsetlin & Michel Regenwetter, 2003. "On the probabilities of correct or incorrect majority preference relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(2), pages 283-306, March.
  • Handle: RePEc:spr:sochwe:v:20:y:2003:i:2:p:283-306
    DOI: 10.1007/s003550200182
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    File URL: http://hdl.handle.net/10.1007/s003550200182
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    Cited by:

    1. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.

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