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Fair representation and a linear Shapley rule

Sascha Kurz, Nicola Maaser and Stefan Napel ()

Games and Economic Behavior, 2018, vol. 108, issue C, 152-161

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 (search for similar items in EconPapers)
JEL-codes: D02 D63 D70 H77 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:152-161