Social Choice and Welfare

, Volume 47, Issue 1, pp 1–24 | Cite as

Pairwise partition graphs and strategy-proof social choice in the exogenous indifference class model

Original Paper
  • 260 Downloads

Abstract

In this paper we consider the exogenous indifference classes model of Barberá and Ehlers (2011) and Sato (2009) and analyze further the relationship between the structure of indifference classes across agents and dictatorship results. The key to our approach is the pairwise partition graph. We provide necessary conditions on these graphs for strategy-proofness and unanimity (or efficiency) to imply dictatorship. These conditions are not sufficient; we also provide separate stronger conditions that are sufficient. A full characterization is obtained in the case of two agents for domains where strategy-proofness and efficiency imply dictatorship.

References

  1. Barberá S, Ehlers L (2011) Free triples, large indifference classes and the majority rule. Soc Choice Welfare 37:559–574CrossRefGoogle Scholar
  2. Dogan E, Sanver MR (2007) On the alternating use of unanimity and surjectivity in the Gibbard-Satterthwaite theorem. Econ Lett 96:140–143CrossRefGoogle Scholar
  3. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601CrossRefGoogle Scholar
  4. Hurwicz L (1972) On Informationally Decentralized Systems. In: McGuire B, Radner R (eds) Decision and organization. North-Holland Press, Amsterdam, pp 297–336Google Scholar
  5. Pápai S (2000) Strategyproof assignment by hierarchical exchange. Econometrica 68:1403–1433CrossRefGoogle Scholar
  6. Pramanik A (2015) Further results on dictatorial domains. Soc Choice Welfare 45:379–398CrossRefGoogle Scholar
  7. Reny P (2001) Arrow’s theorem and the Gibbard–Satterthwaite theorem: a unified approach. Econ Lett 70:99–105CrossRefGoogle Scholar
  8. Sato S (2009) Strategy-proof social choice with exogenous indifference classes. Math Soc Sci 57:48–57CrossRefGoogle Scholar
  9. Sato S (2010) Circular domains. Rev Econ Design 14:331–342CrossRefGoogle Scholar
  10. Sato S (2012) On strategy-proof social choice under categorization. Soc Choice Welfare 38:455–471CrossRefGoogle Scholar
  11. Sato S (2014) A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives. Soc Choice Welfare 42:831–851CrossRefGoogle Scholar
  12. Satterthwaite M (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217CrossRefGoogle Scholar
  13. Satterthwaite M, Sonnenschein H (1981) Strategy-proof allocation mechanism at differentiable. Rev Econ Studies 48:587–597CrossRefGoogle Scholar
  14. Sen A (2001) Another direct proof of the Gibbard–Satterthwaite theorem. Econ Lett 70:381–385CrossRefGoogle Scholar
  15. Svensson L-G (1999) Strategy-proof Allocation of Indivisible Goods. Soc Choice Welfar 16:557–567CrossRefGoogle Scholar
  16. West D (2001) Introduction to graph theory. Prentice Hall, USAGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Social and Economic ResearchOsaka UniversityIbarakiJapan
  2. 2.Indian Statistical InstituteNew DelhiIndia

Personalised recommendations