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One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve

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  • de Mouzon, Olivier
  • Laurent, Thibault
  • Le Breton, Michel

Abstract

The main objective of this paper is to explore and estimate the departure from the “One Man, One Vote” principle in the context of political representation and its consequences for distributive politics. To proceed to the measurement of the inequalities in the representation of territories (geographical under/over representation) or opinions/parties (ideological under/over representation), we import (with some important qualifications and adjustments) the Lorenz curve which is an important tool in the economics of income distribution. We consider subsequently some malapportionment and disproportionality indices. It is applied to the 2010 Electoral College and the French parliamentary and local elections with a special attention to the electoral reform of 2015. In these applications, the Lorenz curve ordering is almost conclusive and consequently the Gini and DK indices are aligned and complement the almost complete ranking derived from Lorenz.

Suggested Citation

  • de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel, 2020. "One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve," TSE Working Papers 20-1089, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:124204
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    References listed on IDEAS

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    1. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    2. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    3. Luc Lauwers & Tom Puyenbroeck, 2006. "The Balinski–Young Comparison of Divisor Methods is Transitive," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 603-606, June.
    4. Zaporozhets, Vera & García-Valiñas, María & Kurz, Sascha, 2016. "Key drivers of EU budget allocation: Does power matter?," European Journal of Political Economy, Elsevier, vol. 43(C), pages 57-70.
    5. Olivier de Mouzon & Thibault Laurent & Michel Le Breton & Issofa Moyouwou, 2020. "“One Man One Vote”. Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May," Post-Print hal-03176208, HAL.
    6. Kauppi, Heikki & Widgren, Mika, 2007. "Voting rules and budget allocation in the enlarged EU," European Journal of Political Economy, Elsevier, vol. 23(3), pages 693-706, September.
    7. Noga Alon & Paul Edelman, 2010. "The inverse Banzhaf problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 371-377, March.
    8. Ansolabehere, Stephen & Gerber, Alan & Snyder, Jim, 2002. "Equal Votes, Equal Money: Court-Ordered Redistricting and Public Expenditures in the American States," American Political Science Review, Cambridge University Press, vol. 96(4), pages 767-777, December.
    9. Arthur F. Veinott, Jr., 1971. "Least d-Majorized Network Flows with Inventory and Statistical Applications," Management Science, INFORMS, vol. 17(9), pages 547-567, May.
    10. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
    11. Stephen Ansolabehere & James M. Snyder & Aaron B. Strauss & Michael M. Ting, 2005. "Voting Weights and Formateur Advantages in the Formation of Coalition Governments," American Journal of Political Science, John Wiley & Sons, vol. 49(3), pages 550-563, July.
    12. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.
    13. Montero, Maria, 2017. "Proportional Payoffs in Legislative Bargaining with Weighted Voting: A Characterization," Quarterly Journal of Political Science, now publishers, vol. 12(3), pages 325-346, October.
    14. Colignatus, Thomas, 2017. "Two conditions for the application of Lorenz curve and Gini coefficient to voting and allocated seats," MPRA Paper 80297, University Library of Munich, Germany, revised 21 Jul 2017.
    15. Laurent, Thibault & Ruiz-Gazen, Anne & Thomas-Agnan, Christine, 2012. "GeoXp: An R Package for Exploratory Spatial Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i02).
    16. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
    17. 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.
    18. Michel Breton & Karine Straeten, 2015. "Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula," Public Choice, Springer, vol. 165(1), pages 103-122, October.
    19. Maaser, Nicola & Stratmann, Thomas, 2016. "Distributional consequences of political representation," European Economic Review, Elsevier, vol. 82(C), pages 187-211.
    20. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
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    More about this item

    Keywords

    Apportionment; Disproportionality; Electoral Justice; Lorenz Curve;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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