Strategy-Proof Voting Rules over Multi-issue Domains with Restricted Preferences

In this paper, we characterize strategy-proof voting rules when the set of alternatives has a multi-issue structure, and the voters' preferences are represented by acyclic CP-nets that follow a common order over issues. Our main result is a simple full characterization of strategy-proof voting rules satisfying non-imposition for a very natural restriction on preferences in multi-issue domains: we show that if the preference domain is lexicographic, then a voting rule satisfying non-imposition is strategy-proof if and only if it can be decomposed into multiple strategy-proof local rules, one for each issue and each setting of the issues preceding it.We also obtain the following variant of Gibbard-Satterthwaite: when there are at least two issues and each of the issues can take at least two values, then there is no non-dictatorial strategy-proof voting rule that satisfies nonimposition, even when the domain of voters' preferences is restricted to linear orders that are consistent with acyclic CP-nets following a common order over issues. This impossibility result follows from either one of two more general new impossibility results we obtained, which are not included in this paper due to the space constraint.

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

[2]  Lirong Xia,et al.  Strongly Decomposable Voting Rules on Multiattribute Domains , 2007, AAAI.

[3]  Lirong Xia,et al.  Sequential composition of voting rules in multi-issue domains , 2009, Math. Soc. Sci..

[4]  Craig Boutilier,et al.  CP-nets: a tool for represent-ing and reasoning with conditional ceteris paribus state-ments , 2004 .

[5]  Toby Walsh,et al.  An Empirical Study of the Manipulability of Single Transferable Voting , 2010, ECAI.

[6]  Noam Nisan,et al.  Elections Can be Manipulated Often , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[7]  Vincent Conitzer,et al.  Generalized scoring rules and the frequency of coalitional manipulability , 2008, EC '08.

[8]  Ariel D. Procaccia,et al.  Average-case tractability of manipulation in voting via the fraction of manipulators , 2007, AAMAS '07.

[9]  Vincent Conitzer,et al.  A sufficient condition for voting rules to be frequently manipulable , 2008, EC '08.

[10]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[11]  Biung-Ghi Ju,et al.  A characterization of strategy-proof voting rules for separable weak orderings , 2003, Soc. Choice Welf..

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

[13]  Ariel D. Procaccia,et al.  Junta distributions and the average-case complexity of manipulating elections , 2006, AAMAS '06.

[14]  Vincent Conitzer,et al.  Voting on Multiattribute Domains with Cyclic Preferential Dependencies , 2008, AAAI.

[15]  Edith Hemaspaandra,et al.  Dichotomy for voting systems , 2005, J. Comput. Syst. Sci..

[16]  Emerson M. S. Niou,et al.  A Problem with Referendums , 2000 .

[17]  Arunava Sen,et al.  Separable Preferences, Decomposability and Strategyproofness , 1999 .

[18]  S. Brams,et al.  The paradox of multiple elections , 1998 .

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

[20]  Vincent Conitzer,et al.  When are elections with few candidates hard to manipulate? , 2007, J. ACM.

[21]  Vincent Conitzer,et al.  A scheduling approach to coalitional manipulation , 2010, EC '10.

[22]  Ronen I. Brafman,et al.  CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements , 2011, J. Artif. Intell. Res..

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

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

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

[26]  Ariel D. Procaccia,et al.  Algorithms for the coalitional manipulation problem , 2008, SODA '08.

[27]  Kim C. Border,et al.  Straightforward Elections, Unanimity, and Phantom Voters , 1983 .

[28]  Piotr Faliszewski,et al.  Copeland voting: ties matter , 2008, AAMAS.

[29]  Toby Walsh,et al.  mCP Nets: Representing and Reasoning with Preferences of Multiple Agents , 2004, AAAI.

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

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

[32]  Vincent Conitzer,et al.  Nonexistence of Voting Rules That Are Usually Hard to Manipulate , 2006, AAAI.

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

[34]  Vincent Conitzer,et al.  Aggregating preferences in multi-issue domains by using maximum likelihood estimators , 2010, AAMAS.

[35]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

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

[37]  Guy Kindler,et al.  The Geometry of Manipulation: A Quantitative Proof of the Gibbard-Satterthwaite Theorem , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[38]  Ariel D. Procaccia,et al.  Complexity of unweighted coalitional manipulation under some common voting rules , 2009, IJCAI 2009.