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Oligarchies in Spatial Environments

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Author Info
Ehlers, Lars
Storcken, Ton

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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. Individual preferences measure distances between alternatives according to the Lp-norm (for a fixed p => 1). When the policy space is multi-dimensional and the set of alternatives has a non-empty interior and it is compact and convex, any quasi-transitive welfare function must be oligarchic. As a corollary we obtain that for transitive welfare functions 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 Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2007-08.

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Length: 17 pages
Date of creation: 2007
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Handle: RePEc:mtl:montde:2007-08

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

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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. Sethuraman, Jay & Teo, Chung-Piaw & Vohra, Rakesh V., 2006. "Anonymous monotonic social welfare functions," Journal of Economic Theory, Elsevier, vol. 128(1), pages 232-254, May. [Downloadable!] (restricted)
  4. Bossert, W. & Weymark, J.A., 1991. "Generalized Median Social Welfare Functions," UBC Departmental Archives 91-29, UBC Department of Economics.
  5. Le Breton, M. & Weymark, J.A., 1991. "Social Choice with Analytic Preferences," G.R.E.Q.A.M. 91a02, Universite Aix-Marseille III.
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  6. EHLERS, Lars & STORCKEN, Ton, 2002. "Arrow's Theorem in Spatial Environments," Cahiers de recherche 2002-03, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  7. Blair, Douglas H. & Pollak, Robert A., 1979. "Collective rationality and dictatorship: The scope of the arrow theorem," Journal of Economic Theory, Elsevier, vol. 21(1), pages 186-194, August. [Downloadable!] (restricted)
  8. 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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