Recognizing 1-Euclidean Preferences: An Alternative Approach

  • Edith Elkind
  • Piotr Faliszewski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)


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.


Feasible Solution Real Line Social Choice Preference Order Stable Match 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barberà, S., Moreno, B.: Top monotonicity: A common root for single peakedness, single crossing and the median voter result. Games and Economic Behavior 73(2), 345–359 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bartholdi III, J., Trick, M.: Stable matching with preferences derived from a psychological model. Operations Research Letters 5(4), 165–169 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Betzler, N., Slinko, A., Uhlmann, J.: On the computation of fully proportional representation. Journal of Artificial Intelligence Research 47, 475–519 (2013)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Black, D.: On the rationale of group decision-making. Journal of Political Economy 56(1), 23–34 (1948)CrossRefGoogle Scholar
  5. 5.
    Brandt, F., Brill, M., Hemaspaandra, E., Hemaspaandra, L.: Bypassing combinatorial protections: Polynomial-time algorithms for single-peaked electorates. In: AAAI 2010, pp. 715–722 (2010)Google Scholar
  6. 6.
    Bredereck, R., Chen, J., Woeginger, G.: A characterization of the single-crossing domain. Social Choice and Welfare 41(4), 989–998 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Chen, J., Pruhs, K., Woeginger, G.: Characterizations of the one-dimensional Euclidean domain. Manuscript (2014)Google Scholar
  8. 8.
    Elkind, E., Faliszewski, P., Skowron, P.: A characterization of the single-peaked single-crossing domain. In: AAAI 2014 (2014)Google Scholar
  9. 9.
    Elkind, E., Faliszewski, P., Slinko, A.: Clone structures in voters’ preferences. In: ACM EC 2012, pp. 496–513 (2012)Google Scholar
  10. 10.
    Escoffier, B., Lang, J., Öztürk, M.: Single-peaked consistency and its complexity. In: ECAI 2008, pp. 366–370 (2008)Google Scholar
  11. 11.
    Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: The shield that never was: Societies with single-peaked preferences are more open to manipulation and control. Information and Computation 209(2), 89–107 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Grandmont, J.M.: Intermediate preferences and the majority rule. Econometrica 46(2), 317–330 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Hotelling, H.: Stability in competition. Economic Journal 39, 41–57 (1929)CrossRefGoogle Scholar
  14. 14.
    Knoblauch, V.: Recognizing one-dimensional euclidean preference profiles. Journal of Mathematical Economics 46, 1–5 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Mirrlees, J.: An exploration in the theory of optimal income taxation. Review of Economic Studies 38, 175–208 (1971)CrossRefzbMATHGoogle Scholar
  16. 16.
    Moulin, H.: On strategy-proofness and single peakedness. Public Choice 35(4), 437–455 (1980)CrossRefGoogle Scholar
  17. 17.
    Saporiti, A.: Strategy-proofness and single-crossing. Theoretical Economics 4(2), 127–163 (2009)Google Scholar
  18. 18.
    Skowron, P., Yu, L., Faliszewski, P., Elkind, E.: The complexity of fully proportional representation for single-crossing electorates. In: Vöcking, B. (ed.) SAGT 2013. LNCS, vol. 8146, pp. 1–12. Springer, Heidelberg (2013)CrossRefGoogle Scholar

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

Personalised recommendations