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Evaluating the Unfairness of Representation With the Nash Social Welfare Function

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  • Junichiro Wada

    (International College of Arts and Sciences, Yokohama City University, wada@yokohama-cu.ac.jp)

Abstract

Using the Nash product (Nash Social Welfare Function) as a micro foundation, we create a decomposable index to evaluate the unfairness of representation in electoral districts. Using this index, we decompose the factors of such unfairness into apportionment and districting. We explore the situations of New Zealand, the United States, Australia, the United Kingdom, Japan, and Canada. We then provide an integer solution that minimizes the index of the apportionment, which can be obtained by the divisor method (Balinski and Young, 1982) using a logarithmic mean.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jothpo:v:22:y:2010:i:4:p:445-467
    DOI: 10.1177/0951629810375643
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    References listed on IDEAS

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    1. Lauwers, Luc & Van Puyenbroeck, Tom, 2008. "Minimally Disproportional Representation: Generalized Entropy and Stolarsky Mean-Divisor Methods of Apportionment," Working Papers 2008/24, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    3. Theil, Henri, 1969. "The Desired Political Entropy," American Political Science Review, Cambridge University Press, vol. 63(2), pages 521-525, June.
    4. Moshe Koppel & Abraham Diskin, 2009. "Measuring disproportionality, volatility and malapportionment: axiomatization and solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 281-286, August.
    5. Loosemore, John & Hanby, Victor J., 1971. "The Theoretical Limits of Maximum Distortion: Some Analytic Expressions for Electoral Systems," British Journal of Political Science, Cambridge University Press, vol. 1(4), pages 467-477, October.
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    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. Wada, Junichiro & Kamahara, Yuta, 2018. "Studying malapportionment using α-divergence," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 77-89.
    3. Junichiro Wada, 2016. "Apportionment Behind the Veil of Uncertainty," The Japanese Economic Review, Japanese Economic Association, vol. 67(3), pages 348-360, September.

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