# L'espace des phases électoral et les statistiques quantiques.Application à la simulation numérique.

Abstract : We consider different voting scheme giving the
collective choice from the lists ranking the preferences of each voter.
These different methods do not give always the same result and,
consequently, we try to evaluate the frequency of possible conflicts.
For that purpose, an electoral phase space of dimension $N=n!$ (where
$n$ is the number of candidates) is introduced. Thus all possible lists
are taken into account. In this space, we determine the points
corresponding to the votes of $M$ electors. Hypothesis on the
distribution of these points leads to distributions known, in physics,
under the name of Maxwell-Boltzmann and Bose-Einstein. We show how they
can be obtained in a numerical simulation with a special attention to
the case where $N$ or $M$ or both go to infinity. We end the paper with
a study of the frequency of the Condorcet effect'' as a function of
the number of candidates and in the limit of a very large number of
voters.
Keywords :

https://halshs.archives-ouvertes.fr/halshs-00003973
Contributor : Jean-Louis Rouet <>
Submitted on : Sunday, June 19, 2005 - 6:57:40 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, April 1, 2010 - 8:07:53 PM

### Identifiers

• HAL Id : halshs-00003973, version 1

### Citation

Jean-Louis Rouet, Marc Feix. L'espace des phases électoral et les statistiques quantiques.
Application à la simulation numérique.. 2005. ⟨halshs-00003973⟩

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