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An axiomatic theory of political representation


  • Chambers, Christopher P.


We discuss the theory of gerrymandering-proof voting rules. Our approach is axiomatic. We show that, for votes over a binary set of alternatives, any rule that is unanimous, anonymous, and gerrymandering-proof must decide a social outcome 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 the outcome of a vote at the district level can be a composition of a governing body (with two possible parties), we discuss the quasi-proportional rules (characterized by unanimity, anonymity, gerrymandering-proofness, 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 discuss a more general environment, where there may be more than two parties.

Suggested Citation

  • Chambers, Christopher P., 2009. "An axiomatic theory of political representation," Journal of Economic Theory, Elsevier, vol. 144(1), pages 375-389, January.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:375-389

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    References listed on IDEAS

    1. Barbera, Salvador & Sonnenschein, Hugo, 1978. "Preference aggregation with randomized social orderings," Journal of Economic Theory, Elsevier, vol. 18(2), pages 244-254, August.
    2. 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.
    3. McLennan, Andrew, 1980. "Randomized preference aggregation: Additivity of power and strategy proofness," Journal of Economic Theory, Elsevier, vol. 22(1), pages 1-11, February.
    4. Fine, Kit, 1972. "Some Necessary and Sufficient Conditions for Representative Decision on Two Alternatives," Econometrica, Econometric Society, vol. 40(6), pages 1083-1090, November.
    5. 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.
    6. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    7. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-921, July.
    8. Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-284, March.
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    Cited by:

    1. 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.
    2. repec:spr:qualqt:v:51:y:2017:i:4:d:10.1007_s11135-016-0361-y is not listed on IDEAS
    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.


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