Results 1  10
of
27
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 ..."
Abstract

Cited by 48 (13 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 45 (18 self)
 Add to MetaCart
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.
Eliciting singlepeaked preferences using comparison queries
 In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems
, 2007
"... Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to ..."
Abstract

Cited by 26 (4 self)
 Add to MetaCart
Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents’ preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on singlepeaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are singlepeaked is known, or at least one other agent’s complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally singlepeaked preferences. For this case, we show that if the alternatives ’ cardinal positions are known, then an agent’s preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost singlepeaked. 1 1
On the approximability of Dodgson and Young elections
, 2008
"... The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorith ..."
Abstract

Cited by 24 (11 self)
 Add to MetaCart
The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LPbased randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(log m) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in N P have quasipolynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that
Hybrid Elections Broaden ComplexityTheoretic Resistance to Control
, 2006
"... Electoral control refers to attempts by an election’s organizer (“the chair”) to influence the outcome by adding/deleting/partitioning voters or candidates. The groundbreaking work of Bartholdi, Tovey, and Trick [BTT92] on (constructive) control proposes computational complexity as a means of resist ..."
Abstract

Cited by 21 (13 self)
 Add to MetaCart
Electoral control refers to attempts by an election’s organizer (“the chair”) to influence the outcome by adding/deleting/partitioning voters or candidates. The groundbreaking work of Bartholdi, Tovey, and Trick [BTT92] on (constructive) control proposes computational complexity as a means of resisting control attempts: Look for election systems where the chair’s task in seeking control is itself computationally infeasible. We introduce and study a method of combining two or more candidateanonymous election schemes in such a way that the combined scheme possesses all the resistances to control (i.e., all the NPhardnesses of control) possessed by any of its constituents: It combines their strengths. From this and new resistance constructions, we prove for the first time that there exists an election scheme that is resistant to all twenty standard types of electoral control.
Parameterized computational complexity of Dodgson and Young elections
, 2007
"... Abstract. We show that, other than for standard complexity theory with known NPcompleteness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed ..."
Abstract

Cited by 21 (7 self)
 Add to MetaCart
Abstract. We show that, other than for standard complexity theory with known NPcompleteness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixedparameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixedparameter tractability as well as W[2]hardness results depending on the cost model for switching ties. 1
Guarantees for the success frequency of an algorithm for finding Dodgsonelection winners
 In Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science
, 2006
"... Dodgson’s election system elegantly satisfies the Condorcet criterion. However, determining the winner of a Dodgson election is known to be Θ p 2complete ([HHR97], see also [BTT89]), which implies that unless P = NP no polynomialtime solution to this problem exists, and unless the polynomial hiera ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
Dodgson’s election system elegantly satisfies the Condorcet criterion. However, determining the winner of a Dodgson election is known to be Θ p 2complete ([HHR97], see also [BTT89]), which implies that unless P = NP no polynomialtime solution to this problem exists, and unless the polynomial hierarchy collapses to NP the problem is not even in NP. Nonetheless, we prove that when the number of voters is much greater than the number of candidates (although the number of voters may still be polynomial in the number of candidates), a simple greedy algorithm very frequently finds the Dodgson winners in such a way that it “knows” that it has found them, and furthermore the algorithm never incorrectly declares a nonwinner to be a winner. 1
On approximating optimal weighted lobbying, and frequency of correctness versus averagecase polynomial time
, 2007
"... We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is intractable in the sense of parameterized complexity. We provide a ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is intractable in the sense of parameterized complexity. We provide an efficient greedy algorithm that achieves a logarithmic approximation ratio for this problem and even for a more general variant—optimal weighted lobbying. We prove that essentially no better approximation ratio than ours can be proven for this greedy algorithm. The problem of determining Dodgson winners is known to be complete for parallel access to NP [HHR97]. Homan and Hemaspaandra [HH06] proposed an efficient greedy heuristic for finding Dodgson winners with a guaranteed frequency of success, and their heuristic is a “frequently selfknowingly correct algorithm. ” We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently selfknowingly correct polynomialtime algorithm. Furthermore, we study some features of probability weight of correctness with respect to Procaccia and Rosenschein’s junta distributions [PR07]. Key words: approximation, Dodgson elections, election systems, frequently selfknowingly correct algorithms, greedy algorithms, optimal lobbying, preference aggregation.
Bypassing Combinatorial Protections: PolynomialTime Algorithms for Singlepeaked Electorates
, 2010
"... For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central politicalscience model of electorates—singlepeaked preferences—those protections vanish. By using singlepeaked preferences to simplify combinatorial covering challenges, we show that NPhard bribery problems—including those for Kemeny and Llull elections—fall to polynomial time. By using singlepeaked preferences to simplify combinatorial partition challenges, we show that NPhard partitionofvoters problems fall to polynomial time. We furthermore show that for singlepeaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ p 2complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in singlepeaked electorates.
Complexity of the exact domatic number problem and of the exact conveyor flow shop problem
"... Abstract. We prove that the exact versions of the domatic number problem are complete for the levels of the boolean hierarchy over NP. The domatic number problem, which arises in the area of computer networks, is the problem of partitioning a given graph into a maximum number of disjoint dominating ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
Abstract. We prove that the exact versions of the domatic number problem are complete for the levels of the boolean hierarchy over NP. The domatic number problem, which arises in the area of computer networks, is the problem of partitioning a given graph into a maximum number of disjoint dominating sets. This number is called the domatic number of the graph. We prove that the problem of determining whether or not the domatic number of a given graph is exactly one of k given values is complete for BH2k(NP), the 2kth level of the boolean hierarchy over NP. In particular, for k = 1, it is DPcomplete to determine whether or not the domatic number of a given graph equals exactly a given integer. Note that DP = BH2(NP). We obtain similar results for the exact versions of generalized dominating set problems and of the conveyor flow shop problem. Our reductions apply Wagner’s conditions sufficient to prove hardness for the levels of the boolean hierarchy over NP. 1.