Solving Multi-Agent Knapsack Problems Using Incremental Approval Voting

In this paper, we study approval voting for multi-agent knapsack problems under incomplete preference information. The agents consider the same set of feasible knapsacks, implicitly defined by a budget constraint, but they possibly diverge in the utilities they attach to items. Individual utilities being difficult to assess precisely and to compare, we collect approval statements on knapsacks from the agents with the aim of determining the optimal solutions by approval voting. We first propose a search procedure based on mixed-integer programming to explore the space of utilities compatible with the known part of preferences in order to determine or approximate the set of possible approval winners. Then, we propose an incremen-tal procedure combining preference elicitation and search in order to determine the set of approval winners without requiring the full elic-itation of the agents' preferences. Finally, the practical efficiency of these procedures is illustrated by various numerical tests.

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

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

[3]  Ariel D. Procaccia,et al.  Complexity of Strategic Behavior in Multi-Winner Elections , 2008, J. Artif. Intell. Res..

[4]  Piotr Faliszewski,et al.  Finding a collective set of items: From proportional multirepresentation to group recommendation , 2014, Artif. Intell..

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

[6]  Ariel D. Procaccia,et al.  On the complexity of achieving proportional representation , 2008, Soc. Choice Welf..

[7]  Craig Boutilier,et al.  Minimax regret based elicitation of generalized additive utilities , 2007, UAI.

[8]  Ariel D. Procaccia,et al.  Voting almost maximizes social welfare despite limited communication , 2010, Artif. Intell..

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

[10]  D. Marc Kilgour,et al.  Approval Balloting for Multi-winner Elections , 2010 .

[11]  Joel Oren,et al.  Online (Budgeted) Social Choice , 2014, AAAI.

[12]  Douglas Muzzio,et al.  Approval voting , 1983 .

[13]  Piotr Faliszewski,et al.  The complexity of fully proportional representation for single-crossing electorates , 2015, Theor. Comput. Sci..

[14]  Joachim Gudmundsson,et al.  Computational Aspects of Multi-Winner Approval Voting , 2014, MPREF@AAAI.

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

[16]  Ning Ding,et al.  Voting with partial information: what questions to ask? , 2013, AAMAS.

[17]  Patrice Perny,et al.  Incremental Weight Elicitation for Multiobjective State Space Search , 2015, AAAI.

[18]  John R. Chamberlin,et al.  Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule , 1983, American Political Science Review.

[19]  Craig Boutilier,et al.  Constraint-based optimization and utility elicitation using the minimax decision criterion , 2006, Artif. Intell..

[20]  Haris Aziz,et al.  Justified representation in approval-based committee voting , 2014, Social Choice and Welfare.

[21]  Toby Walsh,et al.  Elicitation strategies for soft constraint problems with missing preferences: Properties, algorithms and experimental studies , 2010, Artif. Intell..

[22]  Nadja Betzler,et al.  On the Computation of Fully Proportional Representation , 2011, J. Artif. Intell. Res..

[23]  Craig Boutilier,et al.  Social Choice : From Consensus to Personalized Decision Making , 2011 .

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

[25]  Piotr Faliszewski,et al.  Properties of multiwinner voting rules , 2014, Social Choice and Welfare.

[26]  Patrice Perny,et al.  On Possibly Optimal Tradeoffs in Multicriteria Spanning Tree Problems , 2015, ADT.

[27]  Craig Boutilier,et al.  Multi-Winner Social Choice with Incomplete Preferences , 2013, IJCAI.

[28]  Ariel D. Procaccia,et al.  The Distortion of Cardinal Preferences in Voting , 2006, CIA.

[29]  Burt L. Monroe,et al.  Fully Proportional Representation , 1995, American Political Science Review.

[30]  Ariel D. Procaccia,et al.  Strategyproof Classification with Shared Inputs , 2009, IJCAI.

[31]  Steven J. Brams,et al.  Proportional Representation , 1998 .

[32]  Meir Kalech,et al.  Reaching a joint decision with minimal elicitation of voter preferences , 2014, Inf. Sci..