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Unweighted Coalitional Manipulation Under the Borda Rule Is NPHard
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m − 1 points, the second m − 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complex ..."
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Cited by 32 (2 self)
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The Borda voting rule is a positional scoring rule where, for m candidates, for every vote the first candidate receives m − 1 points, the second m − 2 points and so on. A Borda winner is a candidate with highest total score. It has been a prominent open problem to determine the computational complexity of UNWEIGHTED COALITIONAL MANIPULATION UNDER BORDA: Can one add a certain number of additional votes (called manipulators) to an election such that a distinguished candidate becomes a winner? We settle this open problem by showing NPhardness even for two manipulators and three input votes. Moreover, we discuss extensions and limitations of this hardness result.
Complexity of and algorithms for Borda manipulation
 In
, 2011
"... We prove that it is NPhard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NPhardness, we treat computing a manipulation as an ap ..."
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Cited by 31 (11 self)
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We prove that it is NPhard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NPhardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute manipulations of the Borda rule. Experiments show that these methods significantly outperform the previous best known approximation method. We are able to find optimal manipulations in almost all the randomly generated elections tested. Our results suggest that, whilst computing a manipulation of the Borda rule by a coalition is NPhard, computational complexity may provide only a weak barrier against manipulation in practice.
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.
Is Computational Complexity a Barrier to Manipulation?
"... Abstract. When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an e ..."
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Cited by 4 (0 self)
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Abstract. When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, 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. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational “phase transitions”. Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NPhard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems. 1
Algorithms, Theory
"... In their groundbreaking paper, Bartholdi, Tovey and Trick [1] argued that many wellknown voting rules, such as Plurality, Borda, Copeland and Maximin are easy to manipulate. An important assumption made in that paper is that the manipulator’s goal is to ensure that his preferred candidate is amon ..."
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In their groundbreaking paper, Bartholdi, Tovey and Trick [1] argued that many wellknown voting rules, such as Plurality, Borda, Copeland and Maximin are easy to manipulate. An important assumption made in that paper is that the manipulator’s goal is to ensure that his preferred candidate is among the candidates with the maximum score, or, equivalently, that ties are broken in favor of the manipulator’s preferred candidate. In this paper, we examine the role of this assumption in the easiness results of [1]. We observe that the algorithm presented in [1] extends to all rules that break ties according to a fixed ordering over the candidates. We then show that all scoring rules are easy to manipulate if the winner is selected from all tied candidates uniformly at random. This result extends to Maximin under an additional assumption on the manipulator’s utility function that is inspired by the original model of [1]. In contrast, we show that manipulation becomes hard when arbitrary polynomialtime tiebreaking rules are allowed, both for the rules considered in [1], and for a large class of scoring rules.