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An axiomatic theory of political representation

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Author Info
Chambers, Christoper P.

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

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This paper has been announced in the following NEP Reports: References listed on IDEAS
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  1. Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-84, March. [Downloadable!] (restricted)
  2. Chambers, Christopher P., 2005. "Consistent Representative Democracy," Working Papers 1217, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  3. Ching, S. & Thomson, W., 1993. "Population-Monotonic Solutions in Public Good Economies with Single- Peaked Preferences," RCER Working Papers 362, University of Rochester - Center for Economic Research (RCER).
  4. Thomson, William, 1993. "The replacement principle in public good economies with single-peaked preferences," Economics Letters, Elsevier, vol. 42(1), pages 31-36. [Downloadable!] (restricted)
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