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


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).


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


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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

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