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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 54 (8 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 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 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
Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-peaked Electorates
, 2010
"... For many election systems, bribery (and related) attacks have been shown NP-hard 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 ..."
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Cited by 35 (5 self)
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For many election systems, bribery (and related) attacks have been shown NP-hard 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 political-science model of electorates—single-peaked preferences—those protections vanish. By using singlepeaked preferences to simplify combinatorial covering challenges, we show that NP-hard bribery problems—including those for Kemeny and Llull elections—fall to polynomial time. By using single-peaked preferences to simplify combinatorial partition challenges, we show that NP-hard partitionof-voters problems fall to polynomial time. We furthermore show that for single-peaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ p 2-complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in single-peaked electorates.
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 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
Sincere-strategy preference-based approval voting broadly resists control
- In Proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science
, 2008
"... We study sincere-strategy preference-based approval voting (SP-AV), a system proposed by Brams and Sanver [BS06], with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candid ..."
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Cited by 30 (6 self)
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We study sincere-strategy preference-based approval voting (SP-AV), a system proposed by Brams and Sanver [BS06], with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candidates or voters. SP-AV combines the voters ’ preference rankings with their approvals of candidates, and we adapt it here so as to keep its useful features with respect to approval strategies even in the presence of control actions. We prove that this system is computationally resistant (i.e., the corresponding control problems are NPhard) to 19 out of 22 types of constructive and destructive control. Thus, SP-AV has more resistances to control, by three, than is currently known for any other natural voting system with a polynomial-time winner problem. In particular, SP-AV is (after Copeland voting, see Faliszewski et al. [FHHR08]) the second natural voting system with an easy winner-determination procedure that is known to have full resistance to constructive control, and unlike Copeland voting it in addition displays broad resistance to destructive control. 1
Swap bribery
, 2009
"... Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of chang ..."
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Cited by 29 (11 self)
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Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter’s preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of voting rules, including variants of approval and k-approval, Borda, Copeland, and maximin. 1
Can Approximation Circumvent Gibbard-Satterthwaite?
"... The Gibbard-Satterthwaite Theorem asserts that any reasonable voting rule cannot be strategyproof. A large body of research in AI deals with circumventing this theorem via computational considerations; the goal is to design voting rules that are computationally hard, in the worst-case, to manipulate ..."
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Cited by 25 (7 self)
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The Gibbard-Satterthwaite Theorem asserts that any reasonable voting rule cannot be strategyproof. A large body of research in AI deals with circumventing this theorem via computational considerations; the goal is to design voting rules that are computationally hard, in the worst-case, to manipulate. However, recent work indicates that the prominent voting rules are usually easy to manipulate. In this paper, we suggest a new CS-oriented approach to circumventing Gibbard-Satterthwaite, using randomization and approximation. Specifically, we wish to design strategyproof randomized voting rules that are close, in a standard approximation sense, to prominent score-based (deterministic) voting rules. We give tight lower and upper bounds on the approximation ratio achievable via strategyproof randomized rules with respect to positional scoring rules, Copeland, and Maximin.
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.
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 NP-hard, 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 NP-hard, 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 NP-hard. 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 fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule. 1.
Manipulation of Copeland elections
- In AAMAS-10
, 2010
"... We resolve an open problem regarding the complexity of unweighted coalitional manipulation, namely, the complexity of Copeland α-manipulation 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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Cited by 18 (3 self)
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We resolve an open problem regarding the complexity of unweighted coalitional manipulation, namely, the complexity of Copeland α-manipulation 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 head-to-head 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 α-manipulation is NP-complete 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 NP-complete for α ∈{0, 1}. In addition, we resolve the complexity of Copeland α-manipulation for each rational α ∈ [0, 1] for the case of irrational voters.
