IDEAS home Printed from https://ideas.repec.org/a/sae/jothpo/v10y1998i2p147-178.html
   My bibliography  Save this article

Proportional Representation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0951692898010002001
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0951692898010002001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Steven J. Brams & D. Marc Kilgour & Richard F. Potthoff, 2019. "Multiwinner approval voting: an apportionment approach," Public Choice, Springer, vol. 178(1), pages 67-93, January.
    2. Egor Ianovski, 2022. "Electing a committee with dominance constraints," Annals of Operations Research, Springer, vol. 318(2), pages 985-1000, November.
    3. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
    4. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    5. Martin Lackner & Piotr Skowron, 2017. "Consistent Approval-Based Multi-Winner Rules," Papers 1704.02453, arXiv.org, revised Oct 2019.
    6. Piotr Faliszewski & Arkadii Slinko & Kolja Stahl & Nimrod Talmon, 2018. "Achieving fully proportional representation by clustering voters," Journal of Heuristics, Springer, vol. 24(5), pages 725-756, October.
    7. Wojciech Maciejewski & Wojciech Kordecki, 2017. "A method of assigning a global preference index," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(2), pages 59-75.
    8. Florian Brandl & Dominik Peters, 2019. "An axiomatic characterization of the Borda mean rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 685-707, April.
    9. Kamesh Munagala & Yiheng Shen & Kangning Wang & Zhiyi Wang, 2021. "Approximate Core for Committee Selection via Multilinear Extension and Market Clearing," Papers 2110.12499, arXiv.org.
    10. Begoña Subiza & Josep E. Peris, 2017. "A Representative Committee by Approval Balloting," Group Decision and Negotiation, Springer, vol. 26(5), pages 1029-1040, September.
    11. Klamler, Christian & Pferschy, Ulrich & Ruzika, Stefan, 2012. "Committee selection under weight constraints," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 48-56.
    12. Piotr Faliszewski & Piotr Skowron & Arkadii Slinko & Nimrod Talmon, 2018. "Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 513-550, October.
    13. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    14. Eric Kamwa, 2022. "The Condorcet Loser Criterion in Committee Selection," Working Papers hal-03880064, HAL.
    15. Mostapha Diss & Clinton Gabon Gassi & Eric Kamwa, 2024. "On the price of diversity for multiwinner elections under (weakly) separable scoring rules," Working Papers 2024-02, CRESE.
    16. Adam Graham-Squire & Matthew I. Jones & David McCune, 2024. "New fairness criteria for truncated ballots in multi-winner ranked-choice elections," Papers 2408.03926, arXiv.org.
    17. Anna-Sophie Kurella & Salvatore Barbaro, 2024. "On the Polarization Premium for radical parties in PR electoral systems," Working Papers 2410, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    18. Dan Alger, 2006. "Voting by proxy," Public Choice, Springer, vol. 126(1), pages 1-26, January.
    19. Andreas Darmann & Janosch Döcker & Britta Dorn & Sebastian Schneckenburger, 2022. "Simplified group activity selection with group size constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 169-212, March.
    20. Dominik Peters & Lan Yu & Hau Chan & Edith Elkind, 2022. "Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results," Post-Print hal-03834509, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:jothpo:v:10:y:1998:i:2:p:147-178. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.