Random dictatorship domains

A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in Aswal et al., 2003) are needed to restore random dictatorship and such strengthenings are “almost necessary”.

[1]  Shin Sato,et al.  Circular domains , 2010 .

[2]  Hans Peters,et al.  Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences , 2002, J. Econ. Theory.

[3]  Salvador Barberà,et al.  Voting by committees under constraints , 2005, J. Econ. Theory.

[4]  Fred W. Roush,et al.  Kelly's conjecture , 1989 .

[5]  John Duggan,et al.  A geometric proof of Gibbard's random dictatorship theorem , 1996 .

[6]  Alejandro M. Manelli,et al.  Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly , 2004, J. Econ. Theory.

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

[8]  Arunava Sen,et al.  An extreme point characterization of random strategy-proof social choice functions: The two alternative case , 2012 .

[9]  Aranyak Mehta,et al.  Randomized truthful auctions of digital goods are randomizations over truthful auctions , 2004, EC '04.

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

[11]  Uuganbaatar Ninjbat,et al.  Another direct proof for the Gibbard-Satterthwaite Theorem , 2012 .

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

[13]  Arunava Sen,et al.  A Characterization of Single-Peaked Preferences via Random Social Choice Functions , 2016 .

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

[15]  S. Barberà,et al.  Voting under Constraints , 1997 .

[16]  Arunava Sen,et al.  The Structure of Strategy-Proof Random Social Choice Functions over Product Domains and Lexicographically Separable Preferences ⁄ , 2012 .

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

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

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

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

[21]  Hans Peters,et al.  Probabilistic strategy-proof rules over single-peaked domains , 2013 .

[22]  Shigehiro Serizawa,et al.  Power of Voters and Domain of Preferences Where Voting by Committees Is Strategy-Proof , 1995 .

[23]  H.C.M. de Swart.  Navin Aswal e.a., Dictatorial Domains. [Review of the book Dictatorial Domains (Journal of Economic Theory 22), , 2003] , 2005 .

[24]  M. Remzi Sanver,et al.  On domains that admit well-behaved strategy-proof social choice functions , 2013, J. Econ. Theory.

[25]  Arunava Sen.  The Gibbard random dictatorship theorem: a generalization and a new proof , 2011 .

[26]  A. Gibbard.  Manipulation of Schemes That Mix Voting with Chance , 1977 .

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

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