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 selfselective 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 selfselective 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 wellknown 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 JeanFrancois Laslier and William S. Zwicker},
number = {10101},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Schloss Dagstuhl  LeibnizZentrum fuer Informatik, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2561},
annote = {Keywords: Selfselectivity, Stability, Consequentialism, Ehrhart polynomials}
}
Keywords: 

Selfselectivity, Stability, Consequentialism, Ehrhart polynomials 
Seminar: 

10101  Computational Foundations of Social Choice 
Issue Date: 

2010 
Date of publication: 

20.05.2010 