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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- Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-57, January.
- Milyo, Jeffrey, 2000.
"A problem with Euclidean preferences in spatial models of politics,"
Elsevier, vol. 66(2), pages 179-182, February.
- 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.
- Steven J. Brams & Michael A. Jones & D. Marc Kilgour, 2002.
"Single-Peakedness and Disconnected Coalitions,"
Journal of Theoretical Politics,
, vol. 14(3), pages 359-383, July.
- Philippe De Donder, 2000. "Majority voting solution concepts and redistributive taxation," Social Choice and Welfare, Springer, vol. 17(4), pages 601-627.
- 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.
- 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.
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