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An axiomatic theory of political representation

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  • 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.

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Bibliographic Info

Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1218.

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Length: 30 pages
Date of creation: Mar 2005
Date of revision:
Publication status: Published:
Handle: RePEc:clt:sswopa:1218

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Related research

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

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