Results 1  10
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48
Algorithms for the coalitional manipulation problem
 In The ACMSIAM Symposium on Discrete Algorithms (SODA
, 2008
"... We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Scoring rules, Maximin and Plurality with Runoff, and analyze their windows of error. Specifically, given an instance on ..."
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Cited by 46 (10 self)
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We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Scoring rules, Maximin and Plurality with Runoff, and analyze their windows of error. Specifically, given an instance on which an algorithm fails, we bound the additional power the manipulators need in order to succeed. We finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation. 1
A sufficient condition for voting rules to be frequently manipulable
 In Proceedings of the Ninth ACM Conference on Electronic Commerce (EC
, 2008
"... The GibbardSatterthwaite Theorem states that (in unrestricted settings) any reasonable voting rule is manipulable. Recently, a quantitative version of this theorem was proved by Ehud Friedgut, Gil Kalai, and Noam Nisan: when the number of alternatives is three, for any neutral voting rule that is f ..."
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Cited by 35 (10 self)
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The GibbardSatterthwaite Theorem states that (in unrestricted settings) any reasonable voting rule is manipulable. Recently, a quantitative version of this theorem was proved by Ehud Friedgut, Gil Kalai, and Noam Nisan: when the number of alternatives is three, for any neutral voting rule that is far from any dictatorship, there exists a voter such that a random manipulation—that is, the true preferences and the strategic vote are all drawn i.i.d., uniformly at random—will succeed with a probability of Ω ( 1), where n is the n number of voters. However, it seems that the techniques used to prove this theorem can not be fully extended to more than three alternatives. In this paper, we give a more limited result that does apply to four or more alternatives. We give a sufficient condition for a voting rule to be randomly manipulable with a probability of Ω ( 1) for at least one voter, when the number of alternatives is held n fixed. Specifically, our theorem states that if a voting rule r satisfies 1. homogeneity, 2. anonymity, 3. nonimposition, 4. a cancelingout condition, and 5. there exists a stable profile that is still stable after one given alternative is uniformly moved to different positions; then there exists a voter such that a random manipulation for that voter will succeed with a probability of Ω ( 1). We show that n many common voting rules satisfy these conditions, for example any positional scoring rule, Copeland, STV, maximin, and ranked pairs.
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 32 (5 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.
Llull and Copeland voting computationally resist bribery and control
, 2009
"... Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive con ..."
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Cited by 32 (15 self)
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Control and bribery are settings in which an external agent seeks to influence the outcome of an election. Constructive control of elections refers to attempts by an agent to, via such actions as addition/deletion/partition of candidates or voters, ensure that a given candidate wins. Destructive control refers to attempts by an agent to, via the same actions, preclude a given candidate’s victory. An election system in which an agent can sometimes affect the result and it can be determined in polynomial time on which inputs the agent can succeed is said to be vulnerable to the given type of control. An election system in which an agent can sometimes affect the result, yet in which it is NPhard to recognize the inputs on which the agent can succeed, is said to be resistant to the given type of control. Aside from election systems with an NPhard winner problem, the only systems previously known to be resistant to all the standard control types were highly artificial election systems created by hybridization. This paper studies a parameterized version of Copeland voting, denoted by Copeland α, where the parameter α is a rational number between 0 and 1 that specifies how ties are valued in the pairwise comparisons of candidates. In every previously studied constructive or destructive
A Scheduling Approach to Coalitional Manipulation
"... The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a p ..."
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Cited by 26 (11 self)
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The coalitional manipulation problem is one of the central problems in computational social choice. In this paper we focus on solving the problem under the important family of positional scoring rules, in an approximate sense that was advocated by Zuckerman et al. [SODA 2008]. Our main result is a polynomialtime algorithm with (roughly speaking) the following theoretical guarantee: given a manipulable instance with m alternatives the algorithm finds a successful manipulation with at most m − 2 additional manipulators. Our technique is based on a reduction to the scheduling problem known as QpmtnCmax, along with a novel rounding procedure. We demonstrate that our analysis is tight by establishing a new type of integrality gap. We also resolve a known open question in computational social choice by showing that the coalitional manipulation problem remains (strongly) NPcomplete for positional scoring rules even when votes are unweighted. Finally, we discuss the implications of our results with respect to the question: “Is there a prominent voting rule that is usually hard to manipulate?”
A brief introduction to Fourier analysis on the Boolean cube
 Theory of Computing Library– Graduate Surveys
, 2008
"... Abstract: We give a brief introduction to the basic notions of Fourier analysis on the ..."
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Cited by 22 (3 self)
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Abstract: We give a brief introduction to the basic notions of Fourier analysis on the
The geometry of manipulation: A quantitative proof of the gibbardsatterthwaite theorem
 In Proc. of 51st FOCS Symposium
, 2010
"... We prove a quantitative version of the GibbardSatterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10 −4 ǫ 2 n −3 q −30, where ǫ is the minimal statistical distanc ..."
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Cited by 17 (2 self)
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We prove a quantitative version of the GibbardSatterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10 −4 ǫ 2 n −3 q −30, where ǫ is the minimal statistical distance between f and the family of dictator functions. Our results extend those of [FKN09], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [BO91, CS03, EL05, PR06, CS06]) cannot hide manipulations completely. Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies.
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 17 (4 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