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Proportional Representation

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  • Richard F. Potthoff
  • Steven J. Brams

Abstract

Using a recent article by Monroe as a springboard, we extend and generalize his system of proportional representation (PR) by developing a general method for determining a set of winners from the ballots. Central to our analysis is the use of integer programming, which is a type of linear programming. Under Monroe's system and our generalizations of it, one minimizes total misrepresentation, where misrepresentation is based on approval votes, the rankings of candidates, or other ballot information. Our method allows for a variety of PR systems, including those proposed by Monroe, by Chamberlin and Courant, and by Tullock, as well as a new system we call `hierarchical PR'. Ties, the filling of vacancies, and certain problems of both large and small electorates are all rendered manageable with integer programming. We discuss nonmanipulability, representativeness, and other criteria for selecting a PR system and conclude with some recommendations.

Suggested Citation

  • Richard F. Potthoff & Steven J. Brams, 1998. "Proportional Representation," Journal of Theoretical Politics, , vol. 10(2), pages 147-178, April.
    • Handle: RePEc:sae:jothpo:v:10:y:1998:i:2:p:147-178
    DOI: 10.1177/0951692898010002001
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Steven J. Brams, 1990. "Constrained Approval Voting: A Voting System to Elect a Governing Board," Interfaces, INFORMS, vol. 20(5), pages 67-80, October.
    3. Benoît, Jean-Pierre & Kornhauser, Lewis A., 1994. "Social Choice in a Representative Democracy," American Political Science Review, Cambridge University Press, vol. 88(1), pages 185-192, March.
    4. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    5. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
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    Cited by:

    1. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    2. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    3. Steven J. Brams & Peter C. Fishburn, 2001. "A nail-biting election," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 409-414.
    4. Steven Brams & Michael Hansen & Michael Orrison, 2006. "Dead Heat: The 2006 Public Choice Society Election," Public Choice, Springer, vol. 128(3), pages 361-366, September.

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