Voting with partial information: what questions to ask?

Voting is a way to aggregate individual voters' preferences. Traditionally a voter's preference is represented by a total order on the set of candidates. However, sometimes one may not have complete information about a voter's preference, and in this case, can only model a voter's preference as a partial order. Given this framework, there has been work on computing the possible and necessary winners of a (partial) profile. In this paper, we take a step further, look at sets of questions to ask in order to determine the outcome of such a partial profile. Specifically, we call a set of questions a deciding set for a candidate if the outcome of the vote for the candidate is determined no matter how the questions are answered by the voters, and a possible winning (losing) set if there is a way to answer these questions to make the candidate a winner (loser) of the vote. We discuss some interesting properties about these sets of queries, prove some complexity results about them under some well-known voting rules such as plurality and Borda, and consider their application in vote elicitation.

[1]  Vincent Conitzer,et al.  Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders , 2008, AAAI.

[2]  Yann Chevaleyre,et al.  A Short Introduction to Computational Social Choice , 2007, SOFSEM.

[3]  Craig Boutilier,et al.  Vote Elicitation with Probabilistic Preference Models: Empirical Estimation and Cost Tradeoffs , 2011, ADT.

[4]  Toby Walsh,et al.  Incompleteness and Incomparability in Preference Aggregation , 2007, IJCAI.

[5]  M. Panella.  Associate Editor of the Journal of Computer and System Sciences , 2014 .

[6]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[7]  Vincent Conitzer,et al.  Eliciting single-peaked preferences using comparison queries , 2007, AAMAS '07.

[8]  Jörg Rothe,et al.  Taking the final step to a full dichotomy of the possible winner problem in pure scoring rules , 2010, Inf. Process. Lett..

[9]  G. Gottlob,et al.  Propositional circumscription and extended closed-world reasoning are ΠP2-complete , 1993 .

[10]  Craig Boutilier,et al.  Robust Approximation and Incremental Elicitation in Voting Protocols , 2011, IJCAI.

[11]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[12]  Nadja Betzler,et al.  Towards a dichotomy for the Possible Winner problem in elections based on scoring rules , 2009, J. Comput. Syst. Sci..

[13]  Vincent Conitzer,et al.  Dominating Manipulations in Voting with Partial Information , 2011, AAAI.

[14]  J. Voelz,et al.  Chapter 26 , 2014, Wide Neighborhoods.

[15]  Meir Kalech,et al.  Practical voting rules with partial information , 2010, Autonomous Agents and Multi-Agent Systems.

[16]  Jérôme Lang,et al.  Voting procedures with incomplete preferences , 2005 .

[17]  nominatif de l’habitat,et al.  Definitions , 1964, Innovation Dynamics and Policy in the Energy Sector.

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

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

[20]  Alexander Schrijver,et al.  On the history of the transportation and maximum flow problems , 2002, Math. Program..

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

[22]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .