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21
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.
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 10 (7 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
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 5 (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 2 (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.
The Common Structure of Paradoxes in Aggregation Theory
"... In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of aggregation problems called binary aggregation with integrity ..."
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Cited by 2 (2 self)
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In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of aggregation problems called binary aggregation with integrity constraints. We provide a definition of paradox that is general enough to account for the four cases mentioned, and identify a common structure in the syntactic properties of the rationality assumptions that lie behind such paradoxes. We generalise this observation by providing a full characterisation of the set of rationality assumptions on which the majority rule does not generate a paradox. 1
Paradoxes of Multiple Elections: An Approximation Approach
"... When agents need to make decisions on multiple issues, applying common voting rules becomes computationally hard due to the exponentially large number of alternatives. One computationally efficient solution is to vote on the issues sequentially. In this paper, we investigate how well the winner unde ..."
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Cited by 1 (0 self)
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When agents need to make decisions on multiple issues, applying common voting rules becomes computationally hard due to the exponentially large number of alternatives. One computationally efficient 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 that 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. We show some generalized paradoxes of multiple elections: Sequential voting does not approximate many common voting rules well even when the preferences are Olegal or separable. However, these paradoxes are much alleviated or even completely avoided when the preferences are lexicographic or represented by LPtrees. Our results thus draw a border for conditions under which sequential voting rules, which have extremely low computational and communicational cost, are good approximations of some common voting rules w.r.t. their corresponding scoring functions.
Computational Social Choice: Strategic and Combinatorial Aspects
"... When agents have conflicting preferences over a set of alternatives and they want to make a joint decision, a natural way to do so is by voting. How to design and analyze desirable voting rules has been studied by economists for centuries. In recent decades, technological advances, especially those ..."
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Cited by 1 (1 self)
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When agents have conflicting preferences over a set of alternatives and they want to make a joint decision, a natural way to do so is by voting. How to design and analyze desirable voting rules has been studied by economists for centuries. In recent decades, technological advances, especially those in internet economy, have introduced many new applications for voting theory. For example, we can rate movies based on people’s preferences, as done on many movie recommendation sites. However, in such new applications, we always encounter a large number of alternatives or an overwhelming amount of information, which makes computation in voting process a big challenge. Such challenges have led to a burgeoning area—computational social choice, aiming to address problems in computational aspects of preference representation and aggregation in a multiagent scenario.
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 1 (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
Iterated Majority Voting
"... Abstract. We study a model in which a group of agents make a sequence of collective decisions on whether to remain in the current state of the system or switch to an alternative state, as proposed by one of them. Examples for instantiations of this model include the stepwise refinement of a bill of ..."
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Abstract. We study a model in which a group of agents make a sequence of collective decisions on whether to remain in the current state of the system or switch to an alternative state, as proposed by one of them. Examples for instantiations of this model include the stepwise refinement of a bill of law by means of amendments to be voted on, as well as resource allocation problems, where agents successively alter the current allocation by means of a sequence of deals. We specifically focus on cases where the majority rule is used to make each of the collective decisions, as well as variations of the majority rule where different quotas need to be met to get a proposal accepted. In addition, we allow for cases in which the same proposal may be made more than once. As this can lead to infinite sequences, we investigate the effects of introducing a deadline bounding the number of proposals that can be made. We use both analytical and experimental means to characterise situations in which we can expect to see a convergence effect, in the sense that the expected payoff of each agent will become independent from the initial state of the system, as long as the deadline is chosen large enough. 1
Logic and Social Choice Theory
"... We give an introduction to social choice theory, the formal study of mechanisms for collective decision making, and highlight the role that logic has taken, and continues to take, in its development. The first part of the chapter is devoted to a succinct exposition of the axiomatic method in social ..."
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We give an introduction to social choice theory, the formal study of mechanisms for collective decision making, and highlight the role that logic has taken, and continues to take, in its development. The first part of the chapter is devoted to a succinct exposition of the axiomatic method in social choice theory and covers several of the classical theorems in the field. In the second part we then outline three areas of recent research activity: logics for social choice, social choice in combinatorial domains, and judgment aggregation.