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Fair representation and a linear Shapley rule

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  • Kurz, Sascha
  • Maaser, Nicola
  • Napel, Stefan

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.

Suggested Citation

  • Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:152-161
    DOI: 10.1016/j.geb.2017.10.002
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    Cited by:

    1. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.

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    More about this item

    Keywords

    Shapley value; Institutional design; Two-tier voting; Collective choice; Equal representation; Random order values;
    All these keywords.

    JEL classification:

    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • H77 - Public Economics - - State and Local Government; Intergovernmental Relations - - - Intergovernmental Relations; Federalism

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