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Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of part ..."
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Cited by 48 (13 self)
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Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
A Multivariate Complexity Analysis of Lobbying in Multiple Referenda
"... We extend work by Christian et al. [Review of Economic Design 2007] on lobbying in multiple referenda by first providing a more finegrained analysis of the computational complexity of the NPcomplete LOBBYING problem. Herein, given a binary matrix, the columns represent issues to vote on and the ro ..."
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We extend work by Christian et al. [Review of Economic Design 2007] on lobbying in multiple referenda by first providing a more finegrained analysis of the computational complexity of the NPcomplete LOBBYING problem. Herein, given a binary matrix, the columns represent issues to vote on and the rows correspond to voters making a binary vote on each issue. An issue is approved if a majority of votes has a 1 in the corresponding column. The goal is to get all issues approved by modifying a minimum number of rows to all1rows. In our multivariate complexity analysis, we present a more holistic view on the nature of the computational complexity of LOBBYING, providing both (parameterized) tractability and intractability results, depending on various problem parameterizations to be adopted. Moreover, we show nonexistence results concerning efficient and effective preprocessing for LOBBYING and introduce natural variants such as RESTRICTED LOBBYING and PARTIAL LOBBYING. 1
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Decision Making Under Uncertainty: Social Choice and Manipulation ∗
"... My research seeks insight into the complexity of computational reasoning under uncertain information. I focus on preference aggregation and social choice. Insights in these areas have broader impacts in the areas of complexity theory, autonomous agents, and uncertainty in artificial intelligence. Mo ..."
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My research seeks insight into the complexity of computational reasoning under uncertain information. I focus on preference aggregation and social choice. Insights in these areas have broader impacts in the areas of complexity theory, autonomous agents, and uncertainty in artificial intelligence. Motivation: Planning and reasoning in nondeterministic settings is something that people take for granted every day. We do not know for certain that each small action we choose will succeed or fail, if the actions we choose will lead us to catastrophic consequences or land us safely on the other side of the street. The ability to reason in a domain where actions are not guaranteed to succeed is something that humans do fairly well and machines do not. The field of social choice allows us a rich set of domains and problems within which we can work. A central question
Studies in Computational Aspects of Voting — a Parameterized Complexity Perspective ⋆
"... Abstract. We review NPhard voting problems together with their status in terms of parameterized complexity results. In addition, we survey standard techniques for achieving fixedparameter (in)tractability results in voting. 1 ..."
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Abstract. We review NPhard voting problems together with their status in terms of parameterized complexity results. In addition, we survey standard techniques for achieving fixedparameter (in)tractability results in voting. 1
How to Put Through Your Agenda in Collective Binary Decisions ⋆
"... Abstract. We consider the following decision scenario: a society of voters has to find an agreement on a set of proposals, and every single proposal is to be accepted or rejected. Each voter supports a certain subset of the proposals–the favorite ballot of this voter–and opposes the remaining ones. ..."
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Abstract. We consider the following decision scenario: a society of voters has to find an agreement on a set of proposals, and every single proposal is to be accepted or rejected. Each voter supports a certain subset of the proposals–the favorite ballot of this voter–and opposes the remaining ones. He accepts a ballot if he supports more than half of the proposals in this ballot. The task is to decide whether there exists a ballot approving a set of selected proposals (agenda) such that all voters (or a strict majority of them) accept this ballot. On the negative side both problems are NPcomplete, and on the positive side they are fixedparameter tractable with respect to the total number of proposals or with respect to the total number of voters. We look into further natural parameters and study their influence on the computational complexity of both problems, thereby providing both tractability and intractability results. Furthermore, we provide tight combinatorial bounds on the worstcase size of an accepted ballot in terms of the number of voters. 1