An axiomatic theory of political representation

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An axiomatic theory of political representation

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Chambers, Christopher P.

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Christopher P. Chambers

Abstract

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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Publisher Info
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

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Paper
- Chambers, Christoper P., 2005. "An axiomatic theory of political representation," Working Papers 1218, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Fishburn, Peter C, 1971. "The Theory of Representative Majority Decision," Econometrica, Econometric Society, vol. 39(2), pages 273-84, March. [Downloadable!] (restricted)
Chambers, Christopher P., 2005. "Consistent Representative Democracy," Working Papers 1217, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
Other versions:
- Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March. [Downloadable!] (restricted)
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).
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)
Other versions:
- Thomson, W., 1992. "The Replacement Principle in Public Good Economies with Single-Peaked Preferences," RCER Working Papers 340, University of Rochester - Center for Economic Research (RCER).

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