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URN: urn:nbn:de:0030-drops-25610
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2561/
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Merlin, Vincent ; Diss, Mostapha ; Louichi, Ahmed ; Smaoui, Hatem

On the stability of a scoring rules set under the IAC

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Abstract

A society facing a choice problem has also to choose the voting rule itself from a set of different possible voting rules. In such situations, the consequentialism property allows us to induce voters' preferences on voting rules from preferences over alternatives. A voting rule employed to resolve the society's choice problem is self-selective if it chooses itself when it is also used in choosing the voting rule. A voting rules set is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this paper a society which will make a choice from a set constituted by three alternatives {a, b, c} and a set of the three well-known scoring voting rules {Borda, Plurality, Antiplurality}. Under the Impartial Anonymous Culture assumption (IAC), we will derive a probability for the stability of this triplet of voting rules. We use Ehrhart polynomials in order to solve our problems. This method counts the number of lattice points inside a convex bounded polyhedron (polytope). We discuss briefly recent algorithmic solutions to this method and use it to determine the probability of stabillity of {Borda, Plurality, Antiplurality} set.

BibTeX - Entry

@InProceedings{merlin_et_al:DSP:2010:2561,
  author =	{Vincent Merlin and Mostapha Diss and Ahmed Louichi and Hatem Smaoui},
  title =	{On the stability of a scoring rules set under the IAC},
  booktitle =	{Computational Foundations of Social Choice},
  year =	{2010},
  editor =	{Felix Brandt and Vincent Conitzer and Lane A. Hemaspaandra and Jean-Francois Laslier and William S. Zwicker},
  number =	{10101},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2561},
  annote =	{Keywords: Self-selectivity, Stability, Consequentialism, Ehrhart polynomials}
}

Keywords: Self-selectivity, Stability, Consequentialism, Ehrhart polynomials
Seminar: 10101 - Computational Foundations of Social Choice
Issue Date: 2010
Date of publication: 20.05.2010


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