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33
The shield that never was: Societies with singlepeaked preferences are more open to manipulation and control
 In Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
, 2009
"... Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NPhardness shields, and recently there has been much focus on whether such worstcase hardness protections can be bypassed by fre ..."
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Cited by 39 (14 self)
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Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NPhardness shields, and recently there has been much focus on whether such worstcase hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having singlepeaked preferences, many existing NPhardness results on manipulation and control evaporate. 1
Multimode Control Attacks on Elections
"... In 1992, Bartholdi, Tovey, and Trick [1992] opened the study of control attacks on elections—attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexi ..."
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Cited by 34 (12 self)
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In 1992, Bartholdi, Tovey, and Trick [1992] opened the study of control attacks on elections—attempts to improve the election outcome by such actions as adding/deleting candidates or voters. That work has led to many results on how algorithms can be used to find attacks on elections and how complexitytheoretic hardness results can be used as shields against attacks. However, all the work in this line has assumed that the attacker employs just a single type of attack. In this paper, we model and study the case in which the attacker launches a multipronged (i.e., multimode) attack. We do so to more realistically capture the richness of reallife settings. For example, an attacker might simultaneously try to suppress some voters, attract new voters into the election, and introduce a spoiler candidate. Our model provides a unified framework for such varied attacks, and by constructing polynomialtime multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time. 1
On the computation of fully proportional representation
 JOURNAL OF AI RESEARCH
, 2013
"... We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the “sum of misrepresentations” is minimized. The winner determination problem for both systems is known to be NPhard, hence t ..."
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Cited by 18 (7 self)
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We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the “sum of misrepresentations” is minimized. The winner determination problem for both systems is known to be NPhard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximalmisrepresentationintroducingeffectively two new rules. In the general case these “minimax ” versions of classical rules appeared to be still NPhard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixedparameter tractability for the parameter the number of candidates but fixedparameter intractability for the number of winners. For singlepeaked electorates our results are overwhelmingly positive: we provide polynomialtime algorithms for most of the considered problems. The only rule that remains NPhard for singlepeaked electorates is the classical Monroe rule. 1.
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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Cited by 17 (5 self)
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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.
E.Elkind. Campaign management under approvaldriven voting rules
 In Proc.AAAI11,pages 726–731, Aug.2011
"... Approvallike voting rules, such as sincerestrategy preferencebased approval voting (SPAV), the Bucklin rule, and the Fallback rule have many desirable properties: they are easy to understand, and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we ..."
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Approvallike voting rules, such as sincerestrategy preferencebased approval voting (SPAV), the Bucklin rule, and the Fallback rule have many desirable properties: they are easy to understand, and encourage the candidates to choose electoral platforms that have a broad appeal. In this paper, we investigate both classic and parameterized computational complexity of electoral campaign management under such rules. We focus on two methods that can be used to promote a given candidate: asking voters to move this candidate upwards in their preference order or asking them to change the number of candidates they approve of. We show that finding an optimal campaign management strategy of the first type is easy for both Bucklin and Fallback. In contrast, the second method is computationally hard to implement, even if natural parameters of the problem are small. However, we identify a broad special class of campaign management scenarios that admit a fixedparameter tractable algorithm.
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.
Are There Any Nicely Structured Preference Profiles Nearby?
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We investigate the problem of deciding whether a given preference profile is close to a nicely structured preference profile of a certain type, as for instance singlepeaked, singlecaved, singlecrossing, valuerestricted, bestrestricted, worstrestricted, mediumrestricted, or groupseparable profi ..."
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Cited by 11 (1 self)
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We investigate the problem of deciding whether a given preference profile is close to a nicely structured preference profile of a certain type, as for instance singlepeaked, singlecaved, singlecrossing, valuerestricted, bestrestricted, worstrestricted, mediumrestricted, or groupseparable profiles. We measure this distance by the number of voters or alternatives that have to be deleted so as to reach a nicely structured profile. Our results classify all considered problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial time solvable) and computationally intractable (NPhard) questions.
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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Cited by 10 (6 self)
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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.
Computational aspects of nearly singlepeaked electorates
 In Proceedings of the 26th AAAI Conference on Artificial Intelligence
, 2013
"... Manipulation, bribery, and control are wellstudied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to singlepeaked electorates, these systems suddenly become easy to ..."
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Manipulation, bribery, and control are wellstudied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to singlepeaked electorates, these systems suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra (2011b) studied the complexity of dishonest behavior in nearly singlepeaked electorates. These are electorates that are not singlepeaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding singlepeakedness. We prove that determining whether a given profile is nearly singlepeaked is NPcomplete in many cases. For one case we present a polynomialtime algorithm. Furthermore, we explore the relations between several notions of nearly singlepeakedness.
Cloning in Elections: Finding the Possible Winners
"... We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. ..."
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Cited by 7 (2 self)
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We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote with a block of these new candidates, ranked consecutively. The outcome of the resulting election may then depend onthenumberofclonesaswellasonhoweachvoterordersthecloneswithintheblock. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of common voting rules, characterize the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each clone, and study the complexity of finding a minimumcost cloning manipulation. Finally, we compare cloning with two related problems: the problem of control by adding candidates and the problem of possible (co)winners when new alternatives can join. 1.