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Minimally disproportional representation: generalized entropy and Stolarsky mean-divisor methods of apportionment

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  • Lauwers, Luc
  • Van Puyenbroeck, Tom

Abstract

We study divisor methods, the primary class to solve apportionment problems, based upon Stolarsky means Sαβ. These encompass the five traditional methods. We disclose a one-to-one relation between methods of the form Sα1 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.

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Paper provided by Katholieke Universiteit Leuven in its series Open Access publications from Katholieke Universiteit Leuven with number urn:hdl:123456789/185879.

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Date of creation: Jul 2008
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Handle: RePEc:ner:leuven:urn:hdl:123456789/185879

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Web page: http://www.kuleuven.be

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  1. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
  2. Gelman, Andrew & Katz, Jonathan N. & Bafumi, Joseph, 2002. "Standard Voting Power Indexes Don't Work: An Empirical Analysis," Working Papers 1133, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. James M. Snyder Jr. & Michael M. Ting & Stephen Ansolabehere, 2005. "Legislative Bargaining under Weighted Voting," American Economic Review, American Economic Association, vol. 95(4), pages 981-1004, September.
  4. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer, vol. 19(4), pages 885-900.
  5. Balinski, Michel & Ramirez, Victoriano, 1999. "Parametric methods of apportionment, rounding and production," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 107-122, March.
  6. Felsenthal, Dan S. & Machover, Moshe, 1999. "Minimizing the mean majority deficit: The second square-root rule," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 25-37, January.
  7. Vani K. Borooah, 2002. "The Proportionality of Electoral Systems: Electoral Welfare and Electoral Inequality," Economics and Politics, Wiley Blackwell, vol. 14(1), pages 83-98.
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