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Recognizing one-dimensional Euclidean preference profiles

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  • Knoblauch, Vicki

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 1 (January)
Pages: 1-5

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Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:1-5

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Spatial elections Preference representation Mechanism design;

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  1. Miguel Angel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," UFAE and IAE Working Papers 656.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Bogomolnaia, Anna & Laslier, Jean-Francois, 2007. "Euclidean preferences," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 87-98, February.
  3. Laslier, J.F., 1995. "Multivariate Analysis of Comparison Matrices," Papers 9504, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  4. Jean-François Laslier, 2003. "Analysing a preference and approval profile," Social Choice and Welfare, Springer, vol. 20(2), pages 229-242, March.
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Cited by:
  1. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
  2. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer, vol. 52(1), pages 103-128, January.

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