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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 57 (9 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.
The shield that never was: Societies with single-peaked 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 NP-hardness shields, and recently there has been much focus on whether such worst-case hardness protections can be bypassed by fre ..."
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Cited by 42 (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 NP-hardness shields, and recently there has been much focus on whether such worst-case 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 single-peaked preferences, many existing NP-hardness 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 33 (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 complexity-theoretic 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 polynomial-time multiprong attack algorithms we prove that for various election systems even such concerted, flexible attacks can be perfectly planned in deterministic polynomial time. 1
Computational Aspects of Approval Voting
, 2009
"... This paper is concerned with the computational aspects of approval voting and some of its variants, with a particular focus on the complexity of problems that model various ways of tampering with the outcome of an election: manipulation, control, and bribery. For example, in control settings, the el ..."
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Cited by 18 (5 self)
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This paper is concerned with the computational aspects of approval voting and some of its variants, with a particular focus on the complexity of problems that model various ways of tampering with the outcome of an election: manipulation, control, and bribery. For example, in control settings, the election’s chair seeks to alter the outcome of an election via control actions such as adding/deleting/partitioning either candidates or voters. In particular, sincere-strategy preference-based approval voting (SP-AV), a variant of approval voting proposed by Brams and Sanver [BS06], is computationally resistant to 19 of the 22 common types of control. Thus, among those natural voting systems for which winner determination is easy, SP-AV is the system currently known to display the broadest resistance to control. We also present the known complexity results for various types of bribery. Finally, we study local search heuristics for minimax approval voting, a variant of approval voting proposed by Brams, Kilgour, and Sanver [BKS04] (see also [BKS07a,BKS07b]) for the purpose of electing a committee of fixed size.
The complexity of voter partition in Bucklin and fallback voting: Solving three open problems
- In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems
, 2011
"... Electoral control models ways of changing the outcome of an election via such actions as adding/deleting/partitioning either candidates or voters. These actions modify an election’s participation structure and aim at either making a favorite candidate win (“constructive control”) or prevent a despis ..."
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Cited by 16 (1 self)
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Electoral control models ways of changing the outcome of an election via such actions as adding/deleting/partitioning either candidates or voters. These actions modify an election’s participation structure and aim at either making a favorite candidate win (“constructive control”) or prevent a despised candidate from winning (“destructive control”). To protect elections from such control attempts, computational complexity has been used to show that electoral control, though not impossible, is computationally prohibitive. Recently, Erdélyi and Rothe [10] proved that Brams and Sanver’s fallback voting [5], a hybrid voting system that combines Bucklin with approval voting, is resistant to each of the standard types of control except five types of voter control. They proved that fallback voting is vulnerable to two
A complexity-of-strategic-behavior comparison between Schulze’s rule and ranked pairs
- In Proc. of 26th AAAI Conference on AI
, 2012
"... Schulze’s rule and ranked pairs are two Condorcet methods that both satisfy many natural axiomatic properties. Schulze’s rule is used in the elections of many organizations, including ..."
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Cited by 16 (0 self)
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Schulze’s rule and ranked pairs are two Condorcet methods that both satisfy many natural axiomatic properties. Schulze’s rule is used in the elections of many organizations, including
Computing the Margin of Victory for Various Voting Rules
, 2012
"... The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been wi ..."
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Cited by 16 (3 self)
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The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines. In this paper, we investigate the computational complexity and (in)approximability of computing the margin of victory for various voting rules, including approval voting, all positional scoring rules (which include Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also prove a dichotomy theorem, which states that for all continuous generalized scoring rules, including all voting rules studied in this paper, either with high probability the margin of victory is Θ ( √ n), or with high probability the margin of victory is Θ(n), wherenis the number of voters. Most of our results are quite positive, suggesting that the margin of victory can be efficiently computed. This sheds some light on designing efficient post-election audits for voting rules beyond the plurality rule.
E.Elkind. Campaign management under approval-driven voting rules
- In Proc.AAAI-11,pages 726–731, Aug.2011
"... Approval-like voting rules, such as sincere-strategy prefe-rence-based approval voting (SP-AV), 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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Cited by 12 (7 self)
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Approval-like voting rules, such as sincere-strategy prefe-rence-based approval voting (SP-AV), 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 up-wards 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 fixed-parameter tractable algorithm.
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 11 (8 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 polynomial-time algorithms, NP-completeness results, and for many NPcomplete cases, approximation algorithms. Our work shows that for quite a few important cases, either polynomial-time exact algorithms or polynomial-time approximation algorithms exist.
