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The Probability of Conflicts in a U.S. Presidential Type Election

Author

Listed:
  • Vincent Merlin

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Lous Rouet

    (MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Marc Feix

    (MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Lepelley

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, CERESUR - Centre d'Etudes et de Recherches Economique et Sociales de l'Université de La Réunion - UR - Université de La Réunion)

Abstract

In a two candidate election, it might be that a candidatewins in a majority of districts while he gets less vote thanhis opponent in the whole country. In Social Choice Theory, this situation is known asthe compound majority paradox, or the referendum paradox.Although occurrences of such paradoxical results have been observed worldwide in political elections(e.g. United States, United Kingdom, France),no study evaluates theoretically the likelihood of such situations.In this paper, we propose four probability models in order to tackle this issue, forthe case where each district has the same population.For a divided electorate, our resultsprove that the likelihood of this paradox rapidly tends to 20% when the numberof districts increases.This probability decreases with the number of states when a candidate receivessignificatively more vote than his opponent over the whole country.

Suggested Citation

  • Vincent Merlin & Jean-Lous Rouet & Marc Feix & Dominique Lepelley, 2004. "The Probability of Conflicts in a U.S. Presidential Type Election," Post-Print halshs-00083476, HAL.
    • Handle: RePEc:hal:journl:halshs-00083476
    DOI: 10.1007/s00199-003-0375-2
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