Advertisement

Social Choice and Welfare

, Volume 40, Issue 1, pp 41–63 | Cite as

The relation between monotonicity and strategy-proofness

  • Bettina KlausEmail author
  • Olivier Bochet
Open Access
Original Paper

Abstract

The Muller–Satterthwaite Theorem (J Econ Theory 14:412–418, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller–Satterthwaite (J Econ Theory 14:412–418, 1977) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller–Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new “Muller–Satterthwaite preference domains” (e.g., Proposition 3).

Keywords

Public Good Private Good Preference Domain Social Choice Rule Convex Norm 
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.

Notes

Acknowledgments

The authors thank William Thomson and two anonymous referees for their very valuable comments. B. Klaus thank the Netherlands Organisation for Scientific Research (NWO) for its support under grant VIDI-452-06-013. O. Bochet thank the Swiss National Science Foundation (SNF) and the Netherlands Organisation for Scientific Research (NWO) for their support under, respectively, grants SNF-100014-126954 and VENI-451-07-021.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Berga D, Moreno B (2009) Strategic requirements with indifference: single-peaked versus single-plateaued preferences. Soc Choice Welf 32: 275–298CrossRefGoogle Scholar
  2. Black D (1948) On the rationale of group decision-making. J Polit Econ 56: 23–34CrossRefGoogle Scholar
  3. Border G, Jordan J (1983) Straightforward elections, unanimity and phantom voters. Rev Econ Stud 50: 153–170CrossRefGoogle Scholar
  4. Cantala D (2004) Choosing the level of a public good when agents have an outside option. Soc Choice Welf 22: 491–514CrossRefGoogle Scholar
  5. Dasgupta P, Hammond P, Maskin E (1979) The implementation of social choice rules: some general results on incentive compatibility. Rev Econ Stud 46: 181–216CrossRefGoogle Scholar
  6. Fleurbaey M, Maniquet F (1997) Implementability and horizontal equity imply no-envy. Econometrica 65: 1215–1219CrossRefGoogle Scholar
  7. Le Breton M, Zaporozhets V (2009) On the equivalence of coalitional and individual strategy-proofness properties. Soc Choice Welf 33: 287–309CrossRefGoogle Scholar
  8. Maskin E (1977) Nash equilibrium and welfare optimality. MIT Working PaperGoogle Scholar
  9. Maskin E (1985) Theory of implementation in nash equilibrium. In: Hurwicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization. Cambridge University Press, CambridgeGoogle Scholar
  10. Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66: 23–38CrossRefGoogle Scholar
  11. Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35: 437–455CrossRefGoogle Scholar
  12. Moulin H (1984) Generalized condorcet winners for single peaked and single plateau preferences. Soc Choice Welf 1: 127–147CrossRefGoogle Scholar
  13. Muller E, Satterthwaite MA (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14: 412–418CrossRefGoogle Scholar
  14. Papadopoulos A (2005) Metric spaces, convexity and nonpositive curvature. In: IRMA lectures in mathematics and theoretical physics. European Mathematical Society, ZürichGoogle Scholar
  15. Reny PJ (2001) Arrow’s Theorem and the Gibbard–Satterthwaite Theorem: a unified approach. Econ Lett 70: 99–105CrossRefGoogle Scholar
  16. Satterthwaite M, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48: 587–597CrossRefGoogle Scholar
  17. Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59: 509–519CrossRefGoogle Scholar
  18. Takamiya K (2001) Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets. Math Soc Sci 41: 201–213CrossRefGoogle Scholar
  19. Takamiya K (2003) On strategy-proofness and essentially single-valued cores: a converse result. Soc Choice Welf 20: 77–83CrossRefGoogle Scholar
  20. Takamiya K (2007) Domains of social choice functions on which coalition strategy-proofness and Maskin monotonicity are equivalent. Econ Lett 95: 348–354CrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Faculty of Business and EconomicsUniversity of LausanneLausanneSwitzerland
  2. 2.Department of EconomicsUniversity of BernBernSwitzerland
  3. 3.Maastricht UniversityMaastrichtThe Netherlands

Personalised recommendations