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

Abstract : In a two candidate election, it might be that a candidate
wins in a majority of districts while he gets less vote than
his opponent in the whole country. In Social Choice Theory, this situation is known as
the 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, for
the case where each district has the same population.
For a divided electorate, our results
prove that the likelihood of this paradox rapidly tends to 20% when the number
of districts increases.
This probability decreases with the number of states when a candidate receives
significatively more vote than his opponent over the whole country.
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https://halshs.archives-ouvertes.fr/halshs-00083476
Contributor : Vincent Merlin <>
Submitted on : Friday, June 30, 2006 - 7:25:55 PM
Last modification on : Friday, July 19, 2019 - 6:40:08 PM

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Vincent Merlin, Jean-Lous Rouet, Marc Feix, Dominique Lepelley. The Probability of Conflicts in a U.S. Presidential Type Election. Economic Theory, Springer Verlag, 2004, pp.227-257. ⟨10.1007/s00199-003-0375-2⟩. ⟨halshs-00083476⟩

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