License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.10101.6
URN: urn:nbn:de:0030-drops-25610
URL: http://dagstuhl.sunsite.rwth-aachen.de/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
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: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/opus/volltexte/2010/2561},
URN = {urn:nbn:de:0030-drops-25610},
doi = {10.4230/DagSemProc.10101.6},
annote = {Keywords: Self-selectivity, Stability, Consequentialism, Ehrhart polynomials}
}
Keywords: |
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Self-selectivity, Stability, Consequentialism, Ehrhart polynomials |
Collection: |
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10101 - Computational Foundations of Social Choice |
Issue Date: |
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2010 |
Date of publication: |
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20.05.2010 |