Fair representation and a linear Shapley rule

• 成果类型: Article
• 署名作者: Kurz, Sascha; Maaser, Nicola; Napel, Stefan
• 署名单位: University of Bayreuth; University of Bremen; University of Bayreuth
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.10.002
• 发表日期: 2018
• 页码: 152-161
• 关键词: Shapley value; Institutional design; Two-tier voting; collective choice; Equal representation; Random order values

摘要

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. (C) 2017 Elsevier Inc. All rights reserved.