Eliciting single-peaked preferences using comparison queries

Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents' preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. By contrast, in this paper, we focus on single-peaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are single-peaked is known, or at least one other agent's complete preferences are known. We also show that using a sublinear number of queries will not suffice. Finally, we present experimental results.

[1]  Eithan Ephrati,et al.  Multi-Agent Planning as a Dynamic Search for Social Consensus , 1993, IJCAI.

[2]  Eric Horvitz,et al.  Social Choice Theory and Recommender Systems: Analysis of the Axiomatic Foundations of Collaborative Filtering , 2000, AAAI/IAAI.

[3]  Vincent Conitzer,et al.  Communication complexity of common voting rules , 2005, EC '05.

[4]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[5]  David C. Parkes,et al.  Iterative Combinatorial Auctions , 2006 .

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

[7]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[8]  Craig Boutilier,et al.  Local Utility Elicitation in GAI Models , 2005, UAI.

[9]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[10]  Jörg Rothe,et al.  Exact Complexity of the Winner Problem for Young Elections , 2001, Theory of Computing Systems.

[11]  David C. Parkes,et al.  Applying learning algorithms to preference elicitation , 2004, EC '04.

[12]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[13]  Vincent Conitzer,et al.  Vote elicitation: complexity and strategy-proofness , 2002, AAAI/IAAI.

[14]  T. Sandholm,et al.  Preference Elicitation in Combinatorial Auctions (Extended Abstract) , 2001 .

[15]  Steven J. Brams,et al.  Forming stable coalitions: The process matters , 2003 .

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

[17]  Avrim Blum,et al.  On polynomial-time preference elicitation with value queries , 2003, EC '03.

[18]  Peter Haddawy,et al.  Problem-Focused Incremental Elicitation of Multi-Attribute Utility Models , 1997, UAI.

[19]  Daphne Koller,et al.  Making Rational Decisions Using Adaptive Utility Elicitation , 2000, AAAI/IAAI.

[20]  Eithan Ephrati,et al.  The Clarke Tax as a Consensus Mechanism Among Automated Agents , 1991, AAAI.

[21]  Vincent Conitzer,et al.  Computing Slater Rankings Using Similarities among Candidates , 2006, AAAI.

[22]  M. Trick,et al.  Voting schemes for which it can be difficult to tell who won the election , 1989 .

[23]  Vincent Conitzer,et al.  Towards a Characterization of Polynomial Preference Elicitation with Value Queries in Combinatorial Auctions (Extended Abstract) , 2004, COLT.

[24]  Jérôme Lang,et al.  Vote and Aggregation in Combinatorial Domains with Structured Preferences , 2007, IJCAI.

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

[26]  Craig Boutilier,et al.  A POMDP formulation of preference elicitation problems , 2002, AAAI/IAAI.

[27]  Jérôme Lang,et al.  Single-peaked consistency and its complexity , 2008, ECAI.

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

[29]  Ariel D. Procaccia,et al.  Junta Distributions and the Average-Case Complexity of Manipulating Elections , 2007, J. Artif. Intell. Res..

[30]  Yoram Singer,et al.  Learning to Order Things , 1997, NIPS.

[31]  Steven J. Brams,et al.  Single-Peakedness and Disconnected Coalitions , 2002 .

[32]  Avrim Blum,et al.  Preference Elicitation and Query Learning , 2004, J. Mach. Learn. Res..

[33]  Toby Walsh,et al.  Uncertainty in Preference Elicitation and Aggregation , 2007, AAAI.

[34]  Jörg Rothe,et al.  Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP , 1997, JACM.

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

[36]  Yuval Shahar,et al.  Utility Elicitation as a Classification Problem , 1998, UAI.

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

[38]  Tuomas Sandholm,et al.  Preference elicitation in combinatorial auctions , 2002, EC '01.

[39]  Peter Haddawy,et al.  Toward Case-Based Preference Elicitation: Similarity Measures on Preference Structures , 1998, UAI.