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Arrow's Theorem in Spatial Environments

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Author Info
Ehlers,Lars
Storcken,Ton (METEOR)

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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 is a one-dimensional continuum such a welfare function is determined by a collection of 2 N strictly quasiconcave preferences and a tie-breaking rule. As a corollary 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 quasiconcave. When the policy space is multi-dimensional we establish Arrow''s impossibility theorem. Among others we show that weak Pareto, independence of irrelevant alternatives, andnon-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 Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 006.

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Date of creation: 2001
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Handle: RePEc:dgr:umamet:2001006

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Keywords: microeconomics ;

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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.:
  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. 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)
  9. 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)
  10. 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)
  11. 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)
  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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  1. 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:
  2. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer, vol. 41(2), pages 213-230, November. [Downloadable!] (restricted)
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  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!]
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  4. 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!]
  5. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 2006-01, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  6. 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!]
  7. 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:
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