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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.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 1 (January)
Pages: 375-389

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:375-389
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
  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. Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-84, March.
  4. Pattanaik, Prasanta K & Peleg, Bezalel, 1986. "Distribution of Power under Stochastic Social Choice Rules," Econometrica, Econometric Society, vol. 54(4), pages 909-21, July.
  5. Barbera, Salvador & Sonnenschein, Hugo, 1978. "Preference aggregation with randomized social orderings," Journal of Economic Theory, Elsevier, vol. 18(2), pages 244-254, August.
  6. Fine, Kit, 1972. "Some Necessary and Sufficient Conditions for Representative Decision on Two Alternatives," Econometrica, Econometric Society, vol. 40(6), pages 1083-90, November.
  7. 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.
  8. McLennan, Andrew, 1980. "Randomized preference aggregation: Additivity of power and strategy proofness," Journal of Economic Theory, Elsevier, vol. 22(1), pages 1-11, February.
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