Advertisement

Social Choice and Welfare

, Volume 36, Issue 2, pp 305–322 | Cite as

A characterization of the single-peaked domain

  • Miguel A. Ballester
  • Guillaume HaeringerEmail author
Original Paper

Abstract

We provide in this paper two properties that are both necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad hoc underlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value-restricted preference profiles (Sen, Econometrica 34:491–499, 1966) we also provide necessary and sufficient conditions for a preference profile to be single-caved or group-separable. Our results show that for single-peaked, single-caved and group-separable profiles it is sufficient to restrict to profiles containing of either three individuals and three alternatives or two individuals and four alternatives.

Keywords

Preference Relation Linear Order Prefer Alternative Social Choice Function Condorcet Winner 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow K (1951) Social choice and individual values. Wiley, New YorkGoogle Scholar
  2. Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59(3): 595–609CrossRefGoogle Scholar
  3. Bartholdi J III, Trick MA (1986) Stable matching with preferences derived from a psychological model. Oper Res Lett 5(4): 165–169CrossRefGoogle Scholar
  4. Black D (1948) On the rationale of group decision making. J Political Econ 56: 23–34CrossRefGoogle Scholar
  5. Black D (1958) The theory of committees and elections. Cambridge University Press, CambridgeGoogle Scholar
  6. Booth KS, Lueker GS (1976) Testing for the consecutive ones property interval graphs and graph planarity using PQ-tree algorithms. J Comput Syst Sci 13(3): 335–379CrossRefGoogle Scholar
  7. Border KC, Jordan JS (1983) Straightforward elections unanimity and phantom voters. Rev Econ Stud 50(1): 153–170CrossRefGoogle Scholar
  8. Bossert W, Peters H (2006) Single-peaked choice. mimeoGoogle Scholar
  9. Demange G (1982) Single-peaked orders on a tree. Math Soc Sci 3(4): 389–396CrossRefGoogle Scholar
  10. DeMarzo PM, Vayanos D, Zwiebel J (2003) Persuasion bias social influence and unidimensional opinions. Q J Econ 118(3): 909–968CrossRefGoogle Scholar
  11. Dummett M, Farquharson R (1961) Stability in voting. Econometrica 29: 33–43CrossRefGoogle Scholar
  12. Fishburn PC (2002) Acyclic sets of linear orders a progress report. Soc Choice Welf 19(2): 431–447CrossRefGoogle Scholar
  13. Inada K-i (1964) A note on the simple majority decision rule. Econometrica 32: 525–531CrossRefGoogle Scholar
  14. Inada K-i (1969) The simple majority rule. Econometrica 37: 490–506CrossRefGoogle Scholar
  15. Klaus B, Peters H, Storcken T (1997) Strategy-proof division of a private good when preferences are single-dipped. Econ Lett 55(3): 339–346CrossRefGoogle Scholar
  16. Knoblauch V (2010) Recognizing one-dimensional Euclidean preference profile. J Math Econ 46: 1–5CrossRefGoogle Scholar
  17. Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35: 437–455CrossRefGoogle Scholar
  18. Moulin H (1984) Generalized condorect-winners for single peaked and single-plateau preferences. Soc Choice Welf 1(1): 127–147CrossRefGoogle Scholar
  19. Nehring K, Puppe C (2006) The structure of strategy-proof social choice: general characterization and possibility results on median spaces. mimeoGoogle Scholar
  20. Pattanaik PK (1970) Sufficient conditions for the existence of a choice set under majority voting. Econometrica 38: 165–170CrossRefGoogle Scholar
  21. Sen A (1966) A possibility theorem on majority decisions. Econometrica 34: 491–499CrossRefGoogle Scholar
  22. Sen A, Pattanaik PK (1969) Necessary and sufficient conditions for rational choice under majority decision. J Econ Theory 1(1970): 178–202CrossRefGoogle Scholar
  23. Spector D (2000) Rational debate and one-dimensional conflict. Q J Econ 115: 181–200CrossRefGoogle Scholar
  24. Trick MA (1989) Recognizing single-peaked preferences on a tree. Math Soc Sci 17(3): 329–334CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Departament d’Economia i d’Història Econòmica and Barcelona Graduate School of EconomicsUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain

Personalised recommendations