Fair Representation and a Linear Shapley Rule

21 Pages Posted: 18 Oct 2016

See all articles by Sascha Kurz

Sascha Kurz

University of Bayreuth

Nicola Maaser

University of Bremen - Department of Economics

Stefan Napel

University of Bayreuth

Date Written: October 18, 2016

Abstract

When delegations to an assembly or council represent differently sized constituencies, they are often allocated voting weights which increase in population numbers (EU Council, US Electoral College, etc.). The Penrose square root rule (PSRR) is the main benchmark for fair representation of all bottom-tier voters in the top-tier decision making body, but rests on the restrictive assumption of independent binary decisions. We consider intervals of alternatives with single-peaked preferences instead, and presume positive correlation of local voters. This calls for a replacement of the PSRR by a linear Shapley rule: representation is fair if the Shapley value of the delegates is proportional to their constituency sizes.

Keywords: Shapley value; institutional design; two-tier voting; collective choice; equal representation; random order values

JEL Classification: D02; D63; D70; H77

Suggested Citation

Kurz, Sascha and Maaser, Nicola and Napel, Stefan, Fair Representation and a Linear Shapley Rule (October 18, 2016). Available at SSRN: https://ssrn.com/abstract=2853993 or http://dx.doi.org/10.2139/ssrn.2853993

Sascha Kurz (Contact Author)

University of Bayreuth ( email )

Universit├Ątsstr. 30
Lehrstuhl f├╝r 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

Nicola Maaser

University of Bremen - Department of Economics ( email )

Bremen, D-28334
Germany

Stefan Napel

University of Bayreuth ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

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