On the stability of a scoring rules set under the IAC

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

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Vincent Merlin
Mostapha Diss
Ahmed Louichi
Hatem Smaoui

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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)


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.
  • Self-selectivity
  • Stability
  • Consequentialism
  • Ehrhart polynomials


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