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Arrow's Theorem in Spatial Environments

  • EHLERS, Lars
  • STORCKEN, Ton

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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File URL: http://hdl.handle.net/1866/371
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-03.

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Length: 34 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:mtl:montde:2002-03
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  1. Lars Ehlers & John A. Weymark, 2001. "Candidate Stability and Nonbinary Social Choice," Vanderbilt University Department of Economics Working Papers 0113, Vanderbilt University Department of Economics.
  2. 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.
  3. 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.
  4. DUTTA, Bhaskar & JACKSON, Matthew O. & LE BRETON, Michel, 1999. "Strategic candidacy and voting procedures," CORE Discussion Papers 1999011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Kim Border, 1984. "An impossibility theorem for spatial models," Public Choice, Springer, vol. 43(3), pages 293-305, January.
  6. Le Breton, M. & Weymark, J.A., 1991. "Social Choice with Analytic Preferences," G.R.E.Q.A.M. 91a02, Universite Aix-Marseille III.
  7. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
  8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  9. Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November.
  10. Kim, K.H. & Roush, F.W., 1984. "Nonmanipulability in two dimensions," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 29-43, August.
  11. 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.
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