Recognizing 1-Euclidean Preferences: An Alternative Approach

  • Edith Elkind
  • Piotr Faliszewski
Conference paper

DOI: 10.1007/978-3-662-44803-8_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)
Cite this paper as:
Elkind E., Faliszewski P. (2014) Recognizing 1-Euclidean Preferences: An Alternative Approach. In: Lavi R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg

Abstract

We consider the problem of detecting whether a given election is 1-Euclidean, i.e., whether voters and candidates can be mapped to points on the real line so that voters’ preferences over the candidates are determined by the Euclidean distance. A recent paper by Knoblauch [14] shows that this problem admits a polynomial-time algorithm. Knoblauch’s approach relies on the fact that a 1-Euclidean election is necessarily single-peaked, and makes use of the properties of the respective candidate order to find a mapping of voters and candidates to the real line. We propose an alternative polynomial-time algorithm for this problem, which is based on the observation that a 1-Euclidean election is necessarily singe-crossing, and we use the properties of the respective voter order to find the desired mapping.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Edith Elkind
    • 1
  • Piotr Faliszewski
    • 2
  1. 1.University of OxfordOxfordUK
  2. 2.AGH UniversityKrakowPoland

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