Arrow's Theorem in Spatial Environments
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.
|Date of creation:||2002|
|Date of revision:|
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- 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).
- Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November.
- Michel Le Breton & John A. Weymark, 2000.
"Social Choice with Analytic Preferences,"
Vanderbilt University Department of Economics Working Papers
0023, Vanderbilt University Department of Economics, revised Mar 2001.
- Le Breton, M. & Weymark, J.A., 1991. "Social Choice with Analytic Preferences," G.R.E.Q.A.M. 91a02, Universite Aix-Marseille III.
- Michel LeBreton & John A. Weymark, 2000. "Social Choice with Analytic Preferences," Econometric Society World Congress 2000 Contributed Papers 1050, Econometric Society.
- 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.
- Kim Border, 1984. "An impossibility theorem for spatial models," Public Choice, Springer, vol. 43(3), pages 293-305, January.
- 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.
- Kim, K.H. & Roush, F.W., 1984. "Nonmanipulability in two dimensions," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 29-43, August.
- H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
- LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
- Lars Ehlers & John A. Weymark, 2003.
"Candidate stability and nonbinary social choice,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 233-243, 09.
- 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.
- John A. Weymark, 2000. "Candidate Stability and Nonbinary Social Choice," Vanderbilt University Department of Economics Working Papers 0029, Vanderbilt University Department of Economics, revised Feb 2001.
- EHLERS, Lars & WEYMARK, John A., 2001. "Candidate Stability and Nonbinary Social Choice," Cahiers de recherche 2001-30, Universite de Montreal, Departement de sciences economiques.
- 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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