Fair representation and a linear Shapley rule

Sascha Kurz; Nicola Maaser; Stefan Napel

doi:10.1016/j.geb.2017.10.002

Fair representation and a linear Shapley rule

Sascha Kurz, Nicola Maaser^*, Stefan Napel

^*Corresponding author for this work

Health Administrative Centre - Economic Department at Health, Project Economi

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

2 Citations (Scopus)

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.

Original language	English
Journal	Games and Economic Behavior
Volume	108
Pages (from-to)	152-161
Number of pages	10
ISSN	0899-8256
DOIs	https://doi.org/10.1016/j.geb.2017.10.002
Publication status	Published - Mar 2018

Keywords

Collective choice
Equal representation
Institutional design
Random order values
Shapley value
Two-tier voting

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10.1016/j.geb.2017.10.002

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title = "Fair representation and a linear Shapley rule",

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 {\textquoteleft}fair representation{\textquoteright} 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.",

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T1 - Fair representation and a linear Shapley rule

AU - Kurz, Sascha

AU - Maaser, Nicola

AU - Napel, Stefan

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - Collective choice

KW - Equal representation

KW - Institutional design

KW - Random order values

KW - Shapley value

KW - Two-tier voting

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DO - 10.1016/j.geb.2017.10.002

M3 - Journal article

AN - SCOPUS:85033475724

SN - 0899-8256

VL - 108

SP - 152

EP - 161

JO - Games and Economic Behavior

JF - Games and Economic Behavior

ER -

Fair representation and a linear Shapley rule

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Keywords

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