IDEAS home Printed from https://ideas.repec.org/p/clt/sswopa/1218.html
   My bibliography  Save this paper

An axiomatic theory of political representation

Author

Listed:
  • Chambers, Christoper P.

Abstract

We discuss the theory of voting rules which are immune to gerrymandering. Our approach is axiomatic. We show that any rule that is unanimous, anonymous, and representative consistent must decide a social alternative as a function of the proportions of agents voting for each alternative, and must either be independent of this proportion, or be in one-to-one correspondence with the proportions. In an extended model in which voters can vote over elements of the unit interval, we introduce and characterize the quasi-proportional rules based on unanimity, anonymity, representative consistency, strict monotonicity, and continuity. We show that we can always (pointwise) approximate a single-member district quota rule with a quasi-proportional rule. We also establish that upon weakening strict monotonicity, the generalized target rules emerge.

Suggested Citation

  • Chambers, Christoper P., 2005. "An axiomatic theory of political representation," Working Papers 1218, California Institute of Technology, Division of the Humanities and Social Sciences.
  • Handle: RePEc:clt:sswopa:1218
    as

    Download full text from publisher

    File URL: http://www.hss.caltech.edu/SSPapers/wp1218.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    2. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-921, July.
    3. Barbera, Salvador & Sonnenschein, Hugo, 1978. "Preference aggregation with randomized social orderings," Journal of Economic Theory, Elsevier, vol. 18(2), pages 244-254, August.
    4. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    5. Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-284, March.
    6. McLennan, Andrew, 1980. "Randomized preference aggregation: Additivity of power and strategy proofness," Journal of Economic Theory, Elsevier, vol. 22(1), pages 1-11, February.
    7. Fine, Kit, 1972. "Some Necessary and Sufficient Conditions for Representative Decision on Two Alternatives," Econometrica, Econometric Society, vol. 40(6), pages 1083-1090, November.
    8. Bandyopadhyay, Taradas & Deb, Rajat & Pattanaik, Prasanta K., 1982. "The structure of coalitional power under probabilistic group decision rules," Journal of Economic Theory, Elsevier, vol. 27(2), pages 366-375, August.
    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. repec:spr:qualqt:v:51:y:2017:i:4:d:10.1007_s11135-016-0361-y is not listed on IDEAS
    2. Clemens Puppe & Attila Tasnádi, 2015. "Axiomatic districting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 31-50, January.
    3. Mihir Bhattacharya, 2016. "Multilevel multidimensional consistent aggregators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 839-861, April.

    More about this item

    Keywords

    gerrymandering; representative systems; proportional representation; social choice; quasi-arithmetic means;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:clt:sswopa:1218. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Victoria Mason). General contact details of provider: http://www.hss.caltech.edu/ss .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.