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36
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 63 (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.
Aggregating Preferences in MultiIssue Domains by Using Maximum Likelihood Estimators
"... In this paper, we study a maximum likelihood estimation (MLE) approach to preference aggregation and voting when the set of alternatives has a multiissue structure, and the voters ’ preferences are represented by CPnets. We first consider multiissue domains in which each issue is binary; for thes ..."
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Cited by 18 (10 self)
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In this paper, we study a maximum likelihood estimation (MLE) approach to preference aggregation and voting when the set of alternatives has a multiissue structure, and the voters ’ preferences are represented by CPnets. We first consider multiissue domains in which each issue is binary; for these, we propose a general family of distancebased noise models, of which give an axiomatic characterization. We then propose a more specific family of natural distancebased noise models that are parameterized by a threshold. We show that computing the winner for the corresponding MLE voting rule is NPhard when the threshold is 1, but can be done in polynomial time when the threshold is equal to the number of issues. Next, we consider general multiissue domains, and study whether and how issuebyissue voting rules and sequential voting rules can be represented by MLEs. We first show that issuebyissue voting rules in which each local rule is itself an MLE (resp. a ranking scoring rule) can be represented by MLEs with a weak (resp. strong) decomposability property. Then, we prove two theorems that state that if the noise model satisfies a very weak decomposability property, then no sequential voting rule that satisfies unanimity can be represented by an MLE, unless the number of voters is bounded. Finally, we propose and study the MLE approach for CPnet aggregators, which take CPnets as input, and output one or more aggregate CPnets. 1
Majorityrulebased preference aggregation on multiattribute domains with structured preferences
 in Proceedings of the Tenth International Joint Conference on Autonomous Agents and MultiAgent Systems (AAMAS
, 2011
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How Many Vote Operations Are Needed to Manipulate a Voting System?
, 2012
"... In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate n votes i.i.d. according to a distribution π, and let n go to infinity, then for any ɛ > 0, ..."
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Cited by 7 (3 self)
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In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate n votes i.i.d. according to a distribution π, and let n go to infinity, then for any ɛ > 0, with probability at least 1 − ɛ, the minimum number of operations that are needed for the strategic individual to achieve her goal falls into one of the following four categories: (1) 0, (2) Θ ( √ n), (3) Θ(n), and (4) ∞. This theorem holds for any set of vote operations, any individual vote distribution π, and any integer generalized scoring rule, which includes (but is not limited to) almost all commonly studied voting rules, e.g., approval voting, all positional scoring rules (including Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also show that many wellstudied types of strategic behavior fall under our framework, including (but not limited to) constructive/destructive manipulation, bribery, and control by adding/deleting votes, margin of victory, and minimum manipulation coalition size. Therefore, our main theorem naturally applies to these problems.
Bribery in Voting Over Combinatorial Domains Is Easy (Extended Abstract)
"... We investigate the computational complexity of finding optimal bribery schemes in voting domains where the candidate set is the Cartesian product of a set of variables and agents ’ preferences are represented as CPnets. We show that, in most cases, the bribery problem is easy. This also holds for s ..."
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Cited by 7 (4 self)
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We investigate the computational complexity of finding optimal bribery schemes in voting domains where the candidate set is the Cartesian product of a set of variables and agents ’ preferences are represented as CPnets. We show that, in most cases, the bribery problem is easy. This also holds for some cases of kapproval, where bribery is difficult in traditional domains.
Aggregating Dependency Graphs into Voting Agendas in MultiIssue Elections
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a ..."
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Cited by 6 (4 self)
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Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multiissue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multiissue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections.
Hypercubewise Preference Aggregation in MultiIssue Domains
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We consider a framework for preference aggregation on multiple binary issues, where agents ’ preferences are represented by (possibly cyclic) CPnets. We focus on the majority aggregation of the individual CPnets, which is the CPnet where the direction of each edge of the hypercube is decided acco ..."
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Cited by 6 (1 self)
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We consider a framework for preference aggregation on multiple binary issues, where agents ’ preferences are represented by (possibly cyclic) CPnets. We focus on the majority aggregation of the individual CPnets, which is the CPnet where the direction of each edge of the hypercube is decided according to the majority rule. First we focus on hypercube Condorcet winners (HCWs); in particular, we show that, assuming a uniform distribution for the CPnets, the probability that there exists at least one HCW is at least 1 − 1/e, and the expected number of HCWs is 1. Our experimental results confirm these results. We also show experimental results under the Impartial Culture assumption. We then generalize a few tournament solutions to select winners from (weighted) majoritarian CPnets, namely Copeland, maximin, and Kemeny. For each of these, we address some social choice theoretic and computational issues.
Multiagent soft constraint aggregation via sequential voting
"... We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables. We assume agents compactly express their preferences over the ca ..."
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Cited by 5 (0 self)
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We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables. We assume agents compactly express their preferences over the candidates via soft constraints. We consider a sequential procedure that chooses one candidate by asking the agents to vote on one variable at a time. While some properties of this procedure have been already studied, here we focus on independence of irrelevant alternatives, nondictatorship, and strategyproofness. Also, we perform an experimental study that shows that the proposed sequential procedure yields a considerable saving in time with respect to a nonsequential approach, while the winners satisfy the agents just as well, independently of the variable ordering and of the presence of coalitions of agents. 1
Approximating common voting rules by sequential voting in multiissue domains. http://people.seas.harvard.edu/ ∼lxia/Files/approx10.pdf
, 2012
"... When agents need to make decisions on multiple issues, one solution is to vote on the issues sequentially. In this paper, we investigate how well the winner under the sequential voting process approximates the winners under some common voting rules. Some common voting rules, including Borda, kappr ..."
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Cited by 4 (2 self)
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When agents need to make decisions on multiple issues, one solution is to vote on the issues sequentially. In this paper, we investigate how well the winner under the sequential voting process approximates the winners under some common voting rules. Some common voting rules, including Borda, kapproval, Copeland, maximin, Bucklin, and Dodgson, admit natural scoring functions that can serve as a basis for approximation results. We focus on multiissue domains where each issue is binary and the agents ’ preferences are Olegal, separable, represented by LPtrees, or lexicographic. Our results show significant improvements in the approximation ratios when the preferences are represented by LPtrees, compared to the approximation ratios when the preferences are Olegal. However, assuming that the preferences are separable (respectively, lexicographic) does not significantly improve the approximation ratios compared to the case where the preferences are Olegal (respectively, are represented by LPtrees).
Counting, Ranking, and Randomly Generating CPnets∗
"... We introduce a method for generating CPnets uniformly at random. As CPnets encode a subset of partial orders, ensuring that we generate samples uniformly at random is not a trivial task. We present algorithms for counting CPnets, ranking and computing the rank of an arbitrary CPnet for a given ..."
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Cited by 3 (3 self)
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We introduce a method for generating CPnets uniformly at random. As CPnets encode a subset of partial orders, ensuring that we generate samples uniformly at random is not a trivial task. We present algorithms for counting CPnets, ranking and computing the rank of an arbitrary CPnet for a given number of nodes, and generating a CPnet given its rank. We also show how to generate all CPnets with a given number of nodes.