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Arrow's Theorem in Spatial Environments

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Author Info
Ehlers, L.
Storcken, T.

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Abstract

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 2002-03.

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Length: 34 pages
Date of creation: 2002
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Handle: RePEc:mtl:montec:2002-03

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Related research
Keywords: Arrow's theorem; independence of irrelevant alternatives;

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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

References listed on IDEAS
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  1. Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November. [Downloadable!] (restricted)
  2. Le Breton, Michel & Weymark, John, 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003. [Downloadable!]
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  3. John A. Weymark, 2000. "Candidate Stability and Nonbinary Social Choice," Working Papers 0029, Department of Economics, Vanderbilt University, revised Feb 2001. [Downloadable!]
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  4. Michel LeBreton & John A. Weymark, 2000. "Social Choice with Analytic Preferences," Econometric Society World Congress 2000 Contributed Papers 1050, Econometric Society. [Downloadable!]
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  5. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December. [Downloadable!] (restricted)
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  6. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-37, July.
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  7. Bossert, W. & Weymark, J.A., 1991. "Generalized Median Social Welfare Functions," UBC Departmental Archives 91-29, UBC Department of Economics.
  8. Duggan, John, 1996. "Arrow's Theorem in Public Good Environments with Convex Technologies," Journal of Economic Theory, Elsevier, vol. 68(2), pages 303-318, February. [Downloadable!] (restricted)
  9. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier. [Downloadable!] (restricted)
  10. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Blackwell Publishing, vol. 50(1), pages 153-70, January. [Downloadable!] (restricted)
  11. Ehlers, Lars, 2001. "Independence axioms for the provision of multiple public goods as options," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 239-250, March. [Downloadable!] (restricted)
  12. Le Breton, M. & Weymark, J.A., 1991. "An Introduction to Arrovian Social Welfare Functions on Economic and Political Domains," UBC Departmental Archives 91-28, UBC Department of Economics.
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Cited by:
(explanations, 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.)

  1. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 2006-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  2. Michel Le Breton & John A. Weymark, 2002. "Arrovian Social Choice Theory on Economic Domains," Working Papers 0206, Department of Economics, Vanderbilt University, revised Sep 2003. [Downloadable!]
    Other versions:
  3. Ehlers, Lars & Storcken, Ton, 2007. "Oligarchies in Spatial Environments," Research Memoranda 042, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  4. Michel Le Breton & John A. Weymark, 2000. "Social Choice with Analytic Preferences," Working Papers 0023, Department of Economics, Vanderbilt University, revised Mar 2001. [Downloadable!]
    Other versions:
  5. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer, vol. 41(2), pages 213-230, November. [Downloadable!] (restricted)
    Other versions:
  6. Perea, Andrés, 2006. "Epistemic Foundations for Backward Induction: An Overview," Research Memoranda 036, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  7. Ehlers, Lars & Storcken, Ton, 2007. "Arrow's Theorem for One-Dimensional Single-Peaked Preferences," Research Memoranda 043, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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