Recognizing one-dimensional Euclidean preference profiles
A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given preference profile has a one-dimensional Euclidean representation and, if so, constructs one. This result has electoral and mechanism design applications.
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- Laslier, J.F., 1995. "Multivariate Analysis of Comparison Matrices," Papers 9504, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- Jean-François Laslier, 2003. "Analysing a preference and approval profile," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(2), pages 229-242, March.
- Eguia, Jon X., 2008. "The Foundations of Spatial Preferences," Working Papers 08-01, C.V. Starr Center for Applied Economics, New York University.
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- Anna Bogomolnaïa & Jean-François Laslier, 2004. "Euclidean preferences," Working Papers hal-00242941, HAL.
- Miguel Angel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," Working Papers 273, Barcelona Graduate School of Economics.
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