2,116 research outputs found

    The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates

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    Many electoral bribery, control, and manipulation problems (which we will refer to in general as "manipulative actions" problems) are NP-hard in the general case. It has recently been noted that many of these problems fall into polynomial time if the electorate is single-peaked (i.e., is polarized along some axis/issue). However, real-world electorates are not truly single-peaked. There are usually some mavericks, and so real-world electorates tend to merely be nearly single-peaked. This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates, for various notions of nearness and various election systems. We provide instances where even one maverick jumps the manipulative-action complexity up to \np-hardness, but we also provide many instances where a reasonable number of mavericks can be tolerated without increasing the manipulative-action complexity.Comment: 35 pages, also appears as URCS-TR-2011-96

    Reinstating Combinatorial Protections for Manipulation and Bribery in Single-Peaked and Nearly Single-Peaked Electorates

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    Understanding when and how computational complexity can be used to protect elections against different manipulative actions has been a highly active research area over the past two decades. A recent body of work, however, has shown that many of the NP-hardness shields, previously obtained, vanish when the electorate has single-peaked or nearly single-peaked preferences. In light of these results, we investigate whether it is possible to reimpose NP-hardness shields for such electorates by allowing the voters to specify partial preferences instead of insisting they cast complete ballots. In particular, we show that in single-peaked and nearly single-peaked electorates, if voters are allowed to submit top-truncated ballots, then the complexity of manipulation and bribery for many voting rules increases from being in P to being NP-complete.Comment: 28 pages; A shorter version of this paper will appear at the 30th AAAI Conference on Artificial Intelligence (AAAI-16

    Complexity of Manipulative Actions When Voting with Ties

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    Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative actions on elections where voters can have ties, extending the definitions of the election systems (when necessary) to handle voters with ties. We show that for natural election systems allowing ties can both increase and decrease the complexity of manipulation and bribery, and we state a general result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201

    Computational Aspects of Nearly Single-Peaked Electorates

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    Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these rules suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the computational complexity of strategic behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. In case the single-peaked axis is given, we show that determining the distance is always possible in polynomial time. Furthermore, we explore the relations between the new notions introduced in this paper and existing notions from the literature.Comment: Published in the Journal of Artificial Intelligence Research (JAIR). A short version of this paper appeared in the proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence (AAAI 2013). An even earlier version appeared in the proceedings of the Fourth International Workshop on Computational Social Choice 2012 (COMSOC 2012

    The Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control

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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.Comment: 38 pages, 2 figure

    Computational Aspects of Strategic Behaviour in Elections with Top-Truncated Ballots

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    Understanding when and how computational complexity can be used to protect elections against different manipulative actions has been a highly active research area over the past two decades. Much of this literature, however, makes the assumption that the voters or agents specify a complete preference ordering over the set of candidates. There are many multiagent systems applications, and even real-world elections, where this assumption is not warranted, and this in turn raises a series of questions on the impact of partial voting on the complexity of manipulative actions. In this thesis, we focus on two of these questions. First, we address the question of how hard it is to manipulate elections when the agents specify only top-truncated ballots. Here, in particular, we look at the weighted manipulation problem---both constructive and destructive manipulation---when the voters are allowed to specify top-truncated ballots, and we provide general results for all scoring rules, for elimination versions of all scoring rules, for the plurality with runoff rule, for a family of election systems known as Copeland^α, and for the maximin protocol. Subsequently, we also look at the impact on complexity of manipulation when there is uncertainty about the non-manipulators' votes. The second question we address is the question on what the impact of top-truncated voting is on the complexity of manipulative actions in electorates with structured preference profiles. In particular, we consider electorates that are single-peaked or nearly single-peaked and we show how, for many voting protocols, allowing top-truncated voting reimposes the NP-hardness shields that normally vanish in such electorates
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