### 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).

Original language | English |
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Pages (from-to) | 41-63 |

Number of pages | 23 |

Journal | Social Choice and Welfare |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

### Keywords

- PREFERENCES
- EQUIVALENCE

## Cite this

Klaus, B. E., & Bochet, O. L. A. (2013). The relation between monotonicity and strategy-proofness.

*Social Choice and Welfare*,*40*(1), 41-63. https://doi.org/10.1007/s00355-011-0586-6