Skip to main content
Log in

Domains, ranges and strategy-proofness: the case of single-dipped preferences

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

We characterize the set of all individual and group strategy-proof rules on the domain of all single-dipped preferences on a line. For rules defined on this domain, and on several of its subdomains, we explore the implications of these strategy-proofness requirements on the maximum size of the rules’ range. We show that when all single-dipped preferences are admissible, the range must contain two alternatives at most. But this bound changes as we consider different subclasses of single-dipped preferences: we provide examples of subdomains admitting strategy-proof rules with larger ranges. We establish exact bounds on the maximal size of strategy-proof functions on each of these domains, and prove that the relationship between the sizes of the subdomains and those of the ranges of strategy-proof functions on them need not be monotonic. Our results exhibit a sharp contrast between the structure of strategy-proof rules defined on subdomains of single-dipped preferences and those defined on subsets of single-peaked ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: when do they coincide?. J Econ Theory 145: 1648–1674

    Article  Google Scholar 

  • Barberà S, Berga D, Moreno B (2011) Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results. Int J Game Theory. doi:10.1007/s00182-011-0305-7

  • Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59: 595–609

    Article  Google Scholar 

  • Ehlers L (2002) Probabilistic division rules and single-dipped preferences. Soc Choice Welf 19: 325–348

    Article  Google Scholar 

  • Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–601

    Article  Google Scholar 

  • Klaus B (2001) Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object. Econ Theory 17: 675–692

    Article  Google Scholar 

  • Klaus B, Peters H, Storcken T (1997) Strategy-proof division of a private good when preferences are single-dipped. Econ Lett 55: 339–346

    Article  Google Scholar 

  • Larsson B, Svensson L-G (2006) Strategy-proof voting on the full preference domain. Math Soc Sci 52(3): 272–287

    Article  Google Scholar 

  • Manjunath V (2010) Efficient and strategy-proof social choice when preferences are single-dipped, Mimeo

  • Manjunath V (2011) Group strategy-proofness and social choice between two alternatives, Mimeo

  • Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35: 437–455

    Article  Google Scholar 

  • Peremans W, Storcken T (1999) Strategy-proofness on single-dipped preferences domains. In: Proceedings of the international conference, logic, game theory, and social choice, pp 296–313

  • Saari D, Valognes F (1999) The geometry of Black’s single peakedness and related conditions. J Math Econ 32: 429–456

    Article  Google Scholar 

  • Satterthwaite M (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–217

    Article  Google Scholar 

  • Sen AK, Pattanaik PK (1969) Necessary and sufficient conditions for rational choice under majority decision. J Econ Theory 1(2): 178–202

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Salvador Barberà.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barberà, S., Berga, D. & Moreno, B. Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc Choice Welf 39, 335–352 (2012). https://doi.org/10.1007/s00355-011-0624-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-011-0624-4

Keywords

Navigation