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Minimally disproportional representation: generalized entropy and Stolarsky Mean-Divisor Methods of Apportionment

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  • Luc Lauwers
  • Tom Van Puyenbroeck

Abstract

We study divisor methods, the primary class to solve apportionment problems, based upon Stolarsky means Saß. These encompass the five traditional methods. We disclose a one-to-one relation between methods of the form Sa1 and aggregate measures of seat/vote disproportionality of the generalized entropy family: using a divisor method based upon such a generalized logarithmic mean coincides with minimizing a generalized entropy inequality measure. The Balinski-Young ‘favoring small states’.-ordering ranks the generalized entropy methods. This framework improves upon an inconsistency in the traditional inequality approach to apportionment problems, which we illustrate by showing that the major rationale of the ‘method of equal proportions’.is consistently preserved by a non-traditional method.

Suggested Citation

  • Luc Lauwers & Tom Van Puyenbroeck, 2008. "Minimally disproportional representation: generalized entropy and Stolarsky Mean-Divisor Methods of Apportionment," Working Papers of Department of Economics, Leuven ces0819, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:ces0819
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    Cited by:

    1. Wada, Junichiro, 2012. "A divisor apportionment method based on the Kolm–Atkinson social welfare function and generalized entropy," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 243-247.
    2. Biró, Péter & Kóczy, László Á. & Sziklai, Balázs, 2015. "Fair apportionment in the view of the Venice Commission’s recommendation," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 32-41.
    3. Junichiro Wada, 2010. "Evaluating the Unfairness of Representation With the Nash Social Welfare Function," Journal of Theoretical Politics, , vol. 22(4), pages 445-467, October.
    4. Wada, Junichiro & Kamahara, Yuta, 2018. "Studying malapportionment using α-divergence," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 77-89.
    5. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," CERS-IE WORKING PAPERS 1716, Institute of Economics, Centre for Economic and Regional Studies.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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