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86
Junta distributions and the averagecase complexity of manipulating elections
 In AAMAS
, 2006
"... Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used N Pha ..."
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Cited by 91 (23 self)
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Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used N Phardness as the complexity measure. Such a worstcase analysis may be an insufficient guarantee of resistance to manipulation. Indeed, we demonstrate that N Phard manipulations may be tractable in the averagecase. For this purpose, we augment the existing theory of averagecase complexity with some new concepts. In particular, we consider elections distributed with respect to junta distributions, which concentrate on hard instances. We use our techniques to prove that scoring protocols are susceptible to manipulation by coalitions, when the number of candidates is constant. 1.
Nonexistence of Voting Rules That Are Usually Hard to Manipulate
, 2006
"... ... problem for multiagent systems, and one general method for doing so is to vote over the alternatives (candidates). Unfortunately, the GibbardSatterthwaite theorem shows that when there are three or more candidates, all reasonable voting rules are manipulable (in the sense that there exist s ..."
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Cited by 76 (6 self)
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... problem for multiagent systems, and one general method for doing so is to vote over the alternatives (candidates). Unfortunately, the GibbardSatterthwaite theorem shows that when there are three or more candidates, all reasonable voting rules are manipulable (in the sense that there exist situations in which a voter would benefit from reporting its preferences insincerely). To circumvent this impossibility result, recent research has investigated whether it is possible to make finding a beneficial manipulation computationally hard. This approach has had some limited success, exhibiting rules under which the problem of finding a beneficial manipulation is NP hard, #Phard, or even PSPACEhard. Thus, under these rules, it is unlikely that a computationally efficient algorithm can be constructed that always finds a beneficial manipulation (when it exists). However, this still does not preclude the existence of an efficient algorithm that often finds a successful manipulation (when it exists). There have been attempts to design a rule under which finding a beneficial manipulation is usually hard, but they have failed. To explain this failure, in this paper, we show that it is in fact impossible to design such a rule, if the rule is also required to satisfy another property: a large fraction of the manipulable instances are both weakly monotone, and allow the manipulators to make either of exactly two candidates win. We argue why one should expect voting rules to have this property, and show experimentally that common voting rules clearly satisfy it. We also discuss approaches for potentially circumventing this impossibility result.
Voting procedures with incomplete preferences
 in Proc. IJCAI05 Multidisciplinary Workshop on Advances in Preference Handling
, 2005
"... We extend the application of a voting procedure (usually defined on complete preference relations over candidates) when the voters ’ preferences consist of partial orders. We define possible (resp. necessary) winners for a given partial preference profile R with respect to a given voting procedure a ..."
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Cited by 72 (13 self)
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We extend the application of a voting procedure (usually defined on complete preference relations over candidates) when the voters ’ preferences consist of partial orders. We define possible (resp. necessary) winners for a given partial preference profile R with respect to a given voting procedure as the candidates being the winners in some (resp. all) of the complete extensions of R. We show that, although the computation of possible and necessary winners may be hard in general case, it is polynomial for the family of positional scoring procedures. We show that the possible and necessary Condorcet winners for a partial preference profile can be computed in polynomial time as well. Lastly, we point out connections to vote manipulation and elicitation. 1
Generalized scoring rules and the frequency of coalitional manipulability
 In Proceedings of the Ninth ACM Conference on Electronic Commerce (EC
, 2008
"... We introduce a class of voting rules called generalized scoring rules. Under such a rule, each vote generates a vector of k scores, and the outcome of the voting rule is based only on the sum of these vectors—more specifically, only on the order (in terms of score) of the sum’s components. This clas ..."
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Cited by 61 (18 self)
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We introduce a class of voting rules called generalized scoring rules. Under such a rule, each vote generates a vector of k scores, and the outcome of the voting rule is based only on the sum of these vectors—more specifically, only on the order (in terms of score) of the sum’s components. This class is extremely general: we do not know of any commonly studied rule that is not a generalized scoring rule. We then study the coalitional manipulation problem for generalized scoring rules. We prove that under certain natural assump), then tions, if the number of manipulators is O(n p) (for any p < 1 2 the probability that a random profile is manipulable is O(n p − 1 2), where n is the number of voters. We also prove that under another set of natural assumptions, if the number of manipulators is Ω(n p) (for any p> 1) and o(n), then the probability that a random pro2 file is manipulable (to any possible winner under the voting rule) is 1 − O(e −Ω(n2p−1)). We also show that common voting rules satisfy these conditions (for the uniform distribution). These results generalize earlier results by Procaccia and Rosenschein as well as even earlier results on the probability of an election being tied.
Hybrid voting protocols and hardness of manipulation
 In Proceedings of the 16th International Symposium on Algorithms and Computation
, 2005
"... This paper addresses the problem of constructing voting protocols that are hard to manipulate. We describe a general technique for obtaining a new protocol by combining two or more base protocols, and study the resulting class of (voteonce) hybrid voting protocols, which also includes most previous ..."
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Cited by 55 (4 self)
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This paper addresses the problem of constructing voting protocols that are hard to manipulate. We describe a general technique for obtaining a new protocol by combining two or more base protocols, and study the resulting class of (voteonce) hybrid voting protocols, which also includes most previously known manipulationresistant protocols. We show that for many choices of underlying base protocols, including some that are easily manipulable, their hybrids are NPhard to manipulate, and demonstrate that this method can be used to produce manipulationresistant protocols with unique combinations of useful features. 1
Elections Can be Manipulated Often
"... The GibbardSatterthwaite theorem states that every nontrivial voting method between at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the GibbardSatterthwaite theorem: a random manipulation by a single random voter will succeed with nonnegligible probab ..."
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Cited by 55 (1 self)
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The GibbardSatterthwaite theorem states that every nontrivial voting method between at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the GibbardSatterthwaite theorem: a random manipulation by a single random voter will succeed with nonnegligible probability for every neutral voting method between 3 alternatives that is far from being a dictatorship.
Computing Shapley values, manipulating value division schemes, and checking core membership in multiissue domains
 IN PROCEEDINGS OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 2004
"... Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computati ..."
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Cited by 53 (7 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computational questions around these solution concepts have received little attention. We study a concise representation of characteristic functions which allows for the agents to be concerned with a number of independent issues that each coalition of agents can address. For example, there may be a set of tasks that the capacityunconstrained agents could undertake, where accomplishing a task generates a certain amount of value (possibly depending on how well the task is accomplished). Given this representation, we show how to quickly compute the Shapley value—a seminal value division scheme that distributes the gains from cooperation fairly in a certain sense. We then show that in (distributed) marginalcontribution based value division schemes, which are known to be vulnerable to manipulation of the order in which the agents are added to the coalition, this manipulation is NPcomplete. Thus, computational complexity serves as a barrier to manipulating the joining order. Finally, we show that given a value division, determining whether some subcoalition has an incentive to break away (in which case we say the division is not in the core) is NPcomplete. So, computational complexity serves to increase the stability of the coalition.
Algorithms for the coalitional manipulation problem
 In The ACMSIAM Symposium on Discrete Algorithms (SODA
, 2008
"... We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Scoring rules, Maximin and Plurality with Runoff, and analyze their windows of error. Specifically, given an instance on ..."
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Cited by 46 (10 self)
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We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Scoring rules, Maximin and Plurality with Runoff, and analyze their windows of error. Specifically, given an instance on which an algorithm fails, we bound the additional power the manipulators need in order to succeed. We finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation. 1
The Complexity of Bribery in Elections
, 2006
"... We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election’s winner? We study this problem for election systems as varied as scorin ..."
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Cited by 45 (18 self)
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We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election’s winner? We study this problem for election systems as varied as scoring protocols and Dodgson voting, and in a variety of settings regarding the nature of the voters, the size of the candidate set, and the specification of the input. We obtain both polynomialtime bribery algorithms and proofs of the intractability of bribery. Our results indicate that the complexity of bribery is extremely sensitive to the setting. For example, we find settings where bribing weighted voters is NPcomplete in general but if weights are represented in unary then the bribery problem is in P. We provide a complete classification of the complexity of bribery for the broad class of elections (including plurality, Borda, kapproval, and veto) known as scoring protocols.
Common Voting Rules as Maximum Likelihood Estimators
 IN UNCERTAINTY IN ARTIFICIAL INTELLIGENCE: PROCEEDINGS OF THE TWENTIETH CONFERENCE (UAI2005
, 2005
"... Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the alternatives. One potential view of voting is the following. The ..."
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Cited by 45 (13 self)
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Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the alternatives. One potential view of voting is the following. There exists a "correct" outcome (winner/ranking), and each voter's vote corresponds to a noisy perception of this correct outcome. If we are given the noise model, then for any vector of votes, we can compute the maximum likelihood estimate of the correct outcome. This maximum likelihood estimate constitutes a voting rule. In this paper, we ask the following question: For which common voting rules does there exist a noise model such that the rule is the maximum likelihood estimate for that noise model? We require that the votes are drawn independently given the correct outcome (we show that without this restriction, all voting rules have the property). We study the question both for the case where outcomes are winners and for the case where outcomes are rankings. In either case, only some of the common voting rules have the property.