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48
On the Complexity of Voting Manipulation under Randomized TieBreaking
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... Computational complexity of voting manipulation is one of the most actively studied topics in the area of computational social choice, starting with the groundbreaking work of [Bartholdi et al., 1989]. Most of the existing work in this area, including that of [Bartholdi et al., 1989], implicitly ass ..."
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Cited by 18 (1 self)
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Computational complexity of voting manipulation is one of the most actively studied topics in the area of computational social choice, starting with the groundbreaking work of [Bartholdi et al., 1989]. Most of the existing work in this area, including that of [Bartholdi et al., 1989], implicitly assumes that whenever several candidates receive the top score with respect to the given voting rule, the resulting tie is broken according to a lexicographic ordering over the candidates. However, till recently, an equally appealing method of tiebreaking, namely, selecting the winner uniformly at random among all tied candidates, has not been considered in the computational social choice literature. The first paper to analyze the complexity of voting manipulation under randomized tiebreaking is [Obraztsova et al., 2011], where the authors provide polynomialtime algorithms for this problem under scoring rules and—under an additional assumption on the manipulator’s utilities— for Maximin. In this paper, we extend the results of [Obraztsova et al., 2011] by showing that finding an optimal vote under randomized tiebreaking is computationally hard for Copeland and Maximin (with general utilities), as well as for STV and Ranked Pairs, but easy for the Bucklin rule and Plurality with Runoff.
Frequent manipulability of elections: The case of two voters
 In Proc. of 4th WINE
, 2008
"... Abstract. The recent result of Friedgut, Kalai and Nisan [9] gives a quantitative version of the GibbardSatterthwaite Theorem regarding manipulation in elections, but holds only for neutral social choice functions and three alternatives. We complement their theorem by proving a similar result regar ..."
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Abstract. The recent result of Friedgut, Kalai and Nisan [9] gives a quantitative version of the GibbardSatterthwaite Theorem regarding manipulation in elections, but holds only for neutral social choice functions and three alternatives. We complement their theorem by proving a similar result regarding ParetoOptimal social choice functions when the number of voters is two. We discuss the implications of our results with respect to the agenda of precluding manipulation in elections by means of computational hardness. 1
Manipulation of Copeland elections
 In AAMAS10
, 2010
"... We resolve an open problem regarding the complexity of unweighted coalitional manipulation, namely, the complexity of Copeland αmanipulation for α ∈{0, 1}. Copeland α, 0 ≤ α ≤ 1, is an election system where for each pair of candidates we check which one is preferred by more voters (i.e., we conduct ..."
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We resolve an open problem regarding the complexity of unweighted coalitional manipulation, namely, the complexity of Copeland αmanipulation for α ∈{0, 1}. Copeland α, 0 ≤ α ≤ 1, is an election system where for each pair of candidates we check which one is preferred by more voters (i.e., we conduct a headtohead majority contest) and we give one point to this candidate and zero to the other. However, in case of a tie both candidates receive α points. In the end, candidates with most points win. It is known [13] that Copeland αmanipulation is NPcomplete for all rational α’s in (0, 1) −{0.5} (i.e., for all the reasonable cases except the three truly interesting ones). In this paper we show that the problem remains NPcomplete for α ∈{0, 1}. In addition, we resolve the complexity of Copeland αmanipulation for each rational α ∈ [0, 1] for the case of irrational voters.
Probabilistic possible winner determination
 In Proc. of 24th AAAI
, 2010
"... We study the computational complexity of the counting version of the POSSIBLEWINNER problem for elections. In the POSSIBLEWINNER problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins ..."
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We study the computational complexity of the counting version of the POSSIBLEWINNER problem for elections. In the POSSIBLEWINNER problem we are given a profile of voters, each with a partial preference order, and ask if there are linear extensions of the votes such that a designated candidate wins. We also analyze a special case of POSSIBLEWINNER, the MANIPULATION problem. We provide polynomialtime algorithms for counting manipulations in a class of scoring protocols and in several other voting rules. We show #Phardness of the counting variant of POSSIBLEWINNER for plurality and veto and give a simple yet general and practically useful randomized algorithm for a variant of POSSIBLEWINNER for all voting rules for which a winner can be computed in polynomial time.
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.
Manipulating Tournaments in Cup and Round Robin Competitions
"... Abstract. In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal ..."
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Abstract. In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial. 1
Dominating Manipulations in Voting with Partial Information
"... We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an in ..."
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We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an information set, a dominating manipulation is a nontruthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator’s information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NPhard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.
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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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.
Weighted Electoral Control
"... www.cs.rochester.edu/∼lane Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we stu ..."
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www.cs.rochester.edu/∼lane Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we study the complexity of controlling the outcome of weighted elections through adding and deleting voters. We obtain polynomialtime algorithms, NPcompleteness results, and for many NPcomplete cases, approximation algorithms. Our work shows that for quite a few important cases, either polynomialtime exact algorithms or polynomialtime approximation algorithms exist.