### 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 (US) |
---|---|

Pages (from-to) | 41-63 |

Number of pages | 23 |

Journal | Social Choice and Welfare |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2013 |

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### ASJC Scopus subject areas

- Social Sciences (miscellaneous)
- Economics and Econometrics

### Cite this

*Social Choice and Welfare*,

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

**The relation between monotonicity and strategy-proofness.** / Klaus, Bettina; Bochet, Olivier.

Research output: Contribution to journal › Article

*Social Choice and Welfare*, vol. 40, no. 1, pp. 41-63. https://doi.org/10.1007/s00355-011-0586-6

}

TY - JOUR

T1 - The relation between monotonicity and strategy-proofness

AU - Klaus, Bettina

AU - Bochet, Olivier

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84872356163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872356163&partnerID=8YFLogxK

U2 - 10.1007/s00355-011-0586-6

DO - 10.1007/s00355-011-0586-6

M3 - Article

AN - SCOPUS:84872356163

VL - 40

SP - 41

EP - 63

JO - Social Choice and Welfare

JF - Social Choice and Welfare

SN - 0176-1714

IS - 1

ER -