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On the stability of a scoring rules set under the IAC Merlin, Vincent Diss, Mostapha Louichi, Ahmed Smaoui, Hatem Self-selectivity Stability Consequentialism Ehrhart polynomials 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vincent Merlin and Mostapha Diss and Ahmed Louichi and Hatem Smaoui 2010 Is Part Of Dagstuhl Seminar Proceedings, Volume 10101, Computational Foundations of Social Choice (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.10101.6 urn:nbn:de:0030-drops-25610 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10101.6 eng https://creativecommons.org/licenses/by/4.0/legalcode