This note is devoted to the question: How restrictive is the assumption that preferences be Euclidean in d dimensions. In particular it is proven that a preference profile with I individuals and A alternatives can be represented by Euclidean utilities with d dimensions if and only if d=min(I,A-1). The paper also describes the systems of A points which allow for the representation of any profile over A alternatives, and provides some results when only strict preferences are considered.
(This abstract was borrowed from another version of this item.)
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References listed on IDEAS
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- Brams, S. J. & Jones, M. A. & Kilgour, M. D., 2001.
"Single-Peakedness and Disconnected Coalitions,"
01-06, C.V. Starr Center for Applied Economics, New York University.
- Jeffrey Milyo, 1999.
"A Problem with Euclidean Preferences in Spatial Models of Politics,"
Discussion Papers Series, Department of Economics, Tufts University
9920, Department of Economics, Tufts University.
- Milyo, Jeffrey, 2000. "A problem with Euclidean preferences in spatial models of politics," Economics Letters, Elsevier, vol. 66(2), pages 179-182, February.
- Laslier, Jean-François, 2006. "Spatial Approval Voting," Political Analysis, Cambridge University Press, vol. 14(02), pages 160-185, March.
- Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
- Gevers, L. & Jacquemin, J. C., 1987. "Redistributive taxation, majority decisions and the minmax set," European Economic Review, Elsevier, vol. 31(1-2), pages 202-211.
- McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
- Philippe De Donder, 2000. "Majority voting solution concepts and redistributive taxation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 601-627.
- Bailey, Michael, 2001. "Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach," Political Analysis, Cambridge University Press, vol. 9(03), pages 192-210, January.
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