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28 Are the Hard Manipulation Problems
 Eds.), Proceedings of the 17th National Conference on AI (AAAI 2002
, 2002
"... Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by misreporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is N ..."
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Voting is a simple mechanism to combine together the preferences of multiple agents. Unfortunately, agents may try to manipulate the result by misreporting their preferences. One barrier that might exist to such manipulation is computational complexity. In particular, it has been shown that it is NPhard to compute how to manipulate a number of different voting rules. However, NPhardness only bounds the worstcase complexity. Recent theoretical results suggest that manipulation may often be easy in practice. In this paper, we show that empirical studies are useful in improving our understanding of this issue. We consider two settings which represent the two types of complexity results that have been identified in this area: manipulation with unweighted votes by a single agent, and manipulation with weighted votes by a coalition of agents. In the first case, we consider Single Transferable Voting (STV), and in the second case, we consider veto voting. STV is one of the few voting rules used in practice where it is NPhard to compute how a single agent can manipulate the result when votes are unweighted. It also appears one of the harder voting rules to manipulate since it involves multiple rounds. On the other hand, veto voting is one of the simplest representatives of voting rules where it is NPhard to compute how a coalition of weighted agents can manipulate the result. In our experiments, we sample a number of distributions of votes including uniform, correlated and real world elections. In many of the elections in our experiments, it was easy to compute how to manipulate the result or to prove that manipulation was impossible. Even when we were able to identify a situation in which manipulation was hard to compute (e.g. when votes are highly correlated and the election is “hung”), we found that the computational difficulty of computing manipulations was somewhat precarious (e.g. with such “hung ” elections, even a single uncorrelated voter was enough to make manipulation easy to compute). 1.
Campaigns for lazy voters: Truncated ballots
 IN PROCEEDINGS OF THE 11TH INTERNATIONAL JOINT CONFERENCE ON AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS. IFAAMAS
, 2012
"... We study elections in which voters may submit partial ballots consisting of truncated lists: each voter ranks some of her top candidates (and possibly some of her bottom candidates) and is indifferent among the remaining ones. Holding elections with such votes requires adapting classical voting rule ..."
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Cited by 15 (8 self)
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We study elections in which voters may submit partial ballots consisting of truncated lists: each voter ranks some of her top candidates (and possibly some of her bottom candidates) and is indifferent among the remaining ones. Holding elections with such votes requires adapting classical voting rules (which expect complete rankings as input) and these adaptations create various opportunities for candidates who want to increase their chances of winning. We provide complexity results regarding planning various kinds of campaigns in such settings, and we study the complexity of the possible winner problem for the case of truncated votes.
L.: Manipulation of Nanson’s and Baldwin’s rules
 Proceedings of the TwentyFifth AAAI Conference on Artificial Intelligence (AAAI 2011
, 2011
"... Nanson’s and Baldwin’s voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NPhard to manipulate either rule with one manipulator, whilst w ..."
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Cited by 12 (8 self)
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Nanson’s and Baldwin’s voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NPhard to manipulate either rule with one manipulator, whilst with weighted votes, it is NPhard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NPhard to manipulate with a single manipulator, Nanson’s and Baldwin’s rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.
New Candidates Welcome! Possible Winners with respect to the Addition of New Candidates
, 2010
"... In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusi ..."
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Cited by 11 (5 self)
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In some voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of the latter problem, focusing on scoring rules, and we give a formal comparison with related problems such as control via adding candidates or cloning.
A smooth transition from powerlessness to absolute power. http://www.cs.cmu.edu/˜arielpro/papers/ phase.pdf
, 2012
"... We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o ( √ n), where n is the number of voters, then the probability that a random ..."
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We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o ( √ n), where n is the number of voters, then the probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is ω ( √ n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size c √ n, and we show that as c goes from zero to infinity, the limiting probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may not be computationally hard in practice. 1
Eliminating the Weakest Link: Making Manipulation Intractable
 In: Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2012
"... Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increase ..."
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Cited by 7 (2 self)
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Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting rules used in practice, the computational complexity increases. For example, it is already known that it is NPhard to compute how a single voter can manipulate the result of single transferable voting(the elimination version of plurality voting). We show here that it is NPhard to compute how a single voter can manipulate the result of the elimination version of veto voting, of the closely related Coombs ’ rule, and of the elimination versions of a general class of scoring rules.
Control complexity in Bucklin and fallback voting
 Computing Research Repository
, 2011
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Parameterized algorithmics for computational social choice: nine research challenges
 Tsinghua Science and Technology
, 2014
"... Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in ..."
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Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multiagent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problemspecific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context.
Coalitional Manipulation for Schulze’s Rule
"... Schulze’s rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulz ..."
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Schulze’s rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulze’s rule: it is computationally vulnerable to manipulation. In particular, we prove that computing an unweighted coalitional manipulation (UCM) is polynomial for any number of manipulators. This result holds for both the unique winner and the cowinner versions of UCM. This resolves an open question in [14]. We also prove that computing a weighted coalitional manipulation (WCM) is polynomial for a bounded number of candidates. Finally, we discuss the relation between the unique winner UCM problem and the cowinner UCM problem and argue that they have substantially different necessary and sufficient conditions for the existence of a successful manipulation.