On domains that admit well-behaved strategy-proof social choice functions

In this paper, we investigate domains that admit “well-behaved” strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982) [13].

[1]  V. Danilov.  The structure of non-manipulable social choice rules on a tree , 1994 .

[2]  An Extended Single Peak Condition in Social Choice , 1978 .

[3]  Klaus Nehring,et al.  Efficient and strategy-proof voting rules: A characterization , 2007, Games Econ. Behav..

[4]  Ehud Kalai,et al.  Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures , 1977 .

[5]  M. Breton,et al.  Separable preferences, strategyproofness, and decomposability , 1999 .

[6]  Faruk Gul,et al.  Generalized Median Voter Schemes and Committees , 1993 .

[7]  Arunava Sen.  Another direct proof of the Gibbard–Satterthwaite Theorem , 2001 .

[8]  Alejandro Saporiti,et al.  Strategy-proofness and single-crossing , 2009 .

[9]  Jordi Massó,et al.  A maximal domain of preferences for strategy-proof, efficient, and simple rules in the division problem , 2004, Soc. Choice Welf..

[10]  Salvador Barberà,et al.  Voting by Committees , 1991 .

[11]  B. Peleg,et al.  Strategy-proof voting schemes with continuous preferences , 1990 .

[12]  D. Black.  On the Rationale of Group Decision-making , 1948, Journal of Political Economy.

[13]  H. Moulin.  Generalized condorcet-winners for single peaked and single-plateau preferences , 1984 .

[14]  Shigehiro Serizawa,et al.  A Maximal Domain for the Existence of Strategy-Proof Rules☆ , 1998 .

[15]  Arunava Sen,et al.  Dictatorial domains , 2003 .

[16]  Hugo Sonnenschein,et al.  Voting By Quota And Committee , 1988 .

[17]  Klaus Nehring,et al.  The structure of strategy-proof social choice - Part I: General characterization and possibility results on median spaces , 2007, J. Econ. Theory.

[18]  Gabrielle Demange,et al.  Single-peaked orders on a tree , 1982, Math. Soc. Sci..

[19]  Guillaume Haeringer,et al.  A Characterization of Single-Peaked Preferences , 2006 .

[20]  E. Savaglio,et al.  Strategy-proofness and single-peackedness in bounded distributive lattices , 2014, 1406.5120.

[21]  H. Moulin.  On strategy-proofness and single peakedness , 1980 .

[22]  Eric Maskin,et al.  Fonctions de Préférence Collective Définies sur des Domaines de Préférence Individuelle Soumis à des Constraintes , 1979 .

[23]  Salvador Barberà,et al.  Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes , 1999 .

[24]  Guillaume Haeringer,et al.  A characterization of the single-peaked domain , 2011, Soc. Choice Welf..

[25]  Arunava Sen,et al.  Tops-only domains , 2011 .

[26]  Souvik Roy,et al.  Implementation in multidimensional domains with ordinal restrictions , 2013 .

[27]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[28]  Rakesh V. Vohra,et al.  Strategy-proof Location on a Network , 2002, J. Econ. Theory.

[29]  Arunava Sen,et al.  Random dictatorship domains , 2012, Games Econ. Behav..

[30]  Ehud Kalai,et al.  Characterization of the private alternatives domains admitting arrow social welfare functions , 1980 .

[31]  Eitan Muller,et al.  Graphs and Anonymous Social Welfare Functions , 1982 .

[32]  Shigehiro Serizawa,et al.  Maximal Domain for Strategy-Proof Rules with One Public Good , 2000, J. Econ. Theory.

[33]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .