Weighted Committee Games

39 Pages Posted: 12 Dec 2017

See all articles by Sascha Kurz

Sascha Kurz

University of Bayreuth

Alexander Mayer

University of Bayreuth - Department of Economics

Stefan Napel

University of Bayreuth

Date Written: December 8, 2017

Abstract

Weighted committee games generalize n-player simple voting games to m ≥ 3 alternatives. The committee's aggregation rule treats votes anonymously but parties, shareholders, members of supranational organizations, etc. differ in their numbers of votes. Infinitely many vote distributions induce only finitely many distinct mappings from preference profiles to winners, i.e., non-equivalent committees. We identify and compare all committees which use Borda, Copeland, plurality or antiplurality rule. Their geometry and differing numbers of equivalence classes - e.g., 51 for Borda vs. 4 for Copeland rule if n = m = 3 - have so far escaped notice.

They determine voting equilibria, the distribution of power and other aspects of collective choice.

Keywords: weighted voting, simple games, social choice, geometry of voting, equivalence classes, Borda rule, Copeland rule, plurality, antiplurality

JEL Classification: D71, C71, C63

Suggested Citation

Kurz, Sascha and Mayer, Alexander and Napel, Stefan, Weighted Committee Games (December 8, 2017). Available at SSRN: https://ssrn.com/abstract=3084703 or http://dx.doi.org/10.2139/ssrn.3084703

Sascha Kurz (Contact Author)

University of Bayreuth ( email )

Universitätsstr. 30
Lehrstuhl für Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
Germany
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)

HOME PAGE: http://www.wm.uni-bayreuth.de/index.php?id=sascha

Alexander Mayer

University of Bayreuth - Department of Economics ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

Stefan Napel

University of Bayreuth ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

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