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On the stability of a scoring rules set under the IAC

Authors: Vincent Merlin, Mostapha Diss, Ahmed Louichi, and Hatem Smaoui

Published in: Dagstuhl Seminar Proceedings, Volume 10101, Computational Foundations of Social Choice (2010)


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.

Cite as

Vincent Merlin, Mostapha Diss, Ahmed Louichi, and Hatem Smaoui. On the stability of a scoring rules set under the IAC. In Computational Foundations of Social Choice. Dagstuhl Seminar Proceedings, Volume 10101, pp. 1-14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{merlin_et_al:DagSemProc.10101.6,
  author =	{Merlin, Vincent and Diss, Mostapha and Louichi, Ahmed and Smaoui, Hatem},
  title =	{{On the stability of a scoring rules set under the IAC}},
  booktitle =	{Computational Foundations of Social Choice},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10101},
  editor =	{Felix Brandt and Vincent Conitzer and Lane A. Hemaspaandra and Jean-Francois Laslier and William S. Zwicker},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10101.6},
  URN =		{urn:nbn:de:0030-drops-25610},
  doi =		{10.4230/DagSemProc.10101.6},
  annote =	{Keywords: Self-selectivity, Stability, Consequentialism, Ehrhart polynomials}
}
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