A distributed social choice protocol for combinatorial domains

In this paper, we study the problem of collective decision-making over combinatorial domains, where the set of possible alternatives is a Cartesian product of (finite) domain values for each of a given set of variables, and these variables are not preferentially independent. Due to the large alternative space, most common rules for social choice cannot be directly applied to compute a winner. In this paper, we introduce a distributed protocol for collective decision-making in combinatorial domains, which enjoys the following desirable properties: (i) the final decision chosen is guaranteed to be a Smith member; (ii) it enables distributed decision-making and works under incomplete information settings, i.e., the agents are not required to reveal their preferences explicitly; (iii) it significantly reduces the amount of dominance testings (individual outcome comparisons) that each agent needs to conduct, as well as the number of pairwise comparisons; (iv) it is sufficiently general and does not restrict the choice of preference representation languages.

[1]  Ryszard Kowalczyk,et al.  Majority-rule-based preference aggregation on multi-attribute domains with CP-nets , 2011, AAMAS.

[2]  Felix A. Fischer,et al.  The Computational Complexity of Choice Sets , 2007, TARK '07.

[3]  Ulrich Endriss,et al.  Conditional Importance Networks: A Graphical Language for Representing Ordinal, Monotonic Preferences over Sets of Goods , 2009, IJCAI.

[4]  Carmel Domshlak,et al.  Hard and soft constraints for reasoning about qualitative conditional preferences , 2006, J. Heuristics.

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

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

[7]  Markus Schulze,et al.  A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method , 2011, Soc. Choice Welf..

[8]  J. Cave,et al.  Cartel quotas under majority rule , 1995 .

[9]  D. Epple,et al.  Interjurisdictional Sorting and Majority Rule: An Empirical Analysis , 2001 .

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

[11]  Fahiem Bacchus,et al.  Graphical models for preference and utility , 1995, UAI.

[12]  Ryszard Kowalczyk,et al.  An Efficient Protocol for Negotiation over Combinatorial Domains with Incomplete Information , 2011, UAI.

[13]  Craig Boutilier,et al.  Bidding Languages for Combinatorial Auctions , 2001, IJCAI.

[14]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[15]  Toby Walsh,et al.  Winner determination in voting trees with incomplete preferences and weighted votes , 2011, Autonomous Agents and Multi-Agent Systems.

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

[17]  Yoav Shoham,et al.  Expected Utility Networks , 1999, UAI.

[18]  Jin Tan,et al.  A Majority Voting Scheme in Wireless Sensor Networks for Detecting Suspicious Node , 2009, 2009 Second International Symposium on Electronic Commerce and Security.

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

[20]  Miroslaw Truszczynski,et al.  The computational complexity of dominance and consistency in CP-nets , 2005, IJCAI.

[21]  Sébastien Konieczny,et al.  Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory , 2005, Eur. J. Oper. Res..

[22]  Benjamin Ward,et al.  Majority rule and allocation , 1961 .

[23]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[24]  Sébastien Konieczny,et al.  DA2 merging operators , 2004, Artif. Intell..

[25]  Jérôme Lang,et al.  Logical Preference Representation and Combinatorial Vote , 2004, Annals of Mathematics and Artificial Intelligence.

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

[27]  Jérôme Lang,et al.  From Preference Representation to Combinatorial Vote , 2002, KR.