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31
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.
AI’s war on manipulation: Are we winning?
 AI MAGAZINE
"... We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections. ..."
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Cited by 54 (8 self)
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We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections.
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.
Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules
, 2010
"... To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This direc ..."
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Cited by 14 (0 self)
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To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, kapproval, and Borda. Generalizing previous NPhardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NPcomplete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2, 1,...,1, 0), while it is solvable in polynomial time for plurality and veto.
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.
Strategyproof voting rules over multiissue domains with restricted preferences
 IN SUBMISSION
, 2009
"... In this paper, we characterize strategyproof voting rules when the set of alternatives has a multiissue structure, and the voters ’ preferences are represented by acyclic CPnets that follow a common order over issues. We show that if the preference domain is lexicographic, then a voting rule sati ..."
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Cited by 9 (6 self)
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In this paper, we characterize strategyproof voting rules when the set of alternatives has a multiissue structure, and the voters ’ preferences are represented by acyclic CPnets that follow a common order over issues. We show that if the preference domain is lexicographic, then a voting rule satisfying nonimposition is strategyproof if and only if it can be decomposed into multiple strategyproof rules, one for each issue and each setting of the issues preceding it. We then prove impossibility theorems for strategyproof voting rules that satisfy nonimposition in two kinds of preference domains: the first result is for supersets of any lexicographic preference domain, and the second is for supersets of any rich preference domain (for a notion of richness introduced by Le Breton and Sen).
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.
Control complexity in Bucklin and fallback voting
 Computing Research Repository
, 2011
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An Empirical Study of Borda Manipulation
"... We study the problem of coalitional manipulation in elections using the unweighted Borda rule. We provide empirical evidence of the manipulability of Borda elections in the form of two new greedy manipulation algorithms based on intuitions from the binpacking and multiprocessor scheduling domains. ..."
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Cited by 6 (3 self)
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We study the problem of coalitional manipulation in elections using the unweighted Borda rule. We provide empirical evidence of the manipulability of Borda elections in the form of two new greedy manipulation algorithms based on intuitions from the binpacking and multiprocessor scheduling domains. Although we have not been able to show that these algorithms beat existing methods in the worstcase, our empirical evaluation shows that they significantly outperform the existing method and are able to find optimal manipulations in the vast majority of the randomly generated elections that we tested. These empirical results provide further evidence that the Borda rule provides little defense against coalitional manipulation. 1