Very Hard Electoral Control Problems

Fitzsimmons, Zack; Hemaspaandra, Edith; Hoover, Alexander; Narváez, David E.

doi:10.1609/aaai.v33i01.33011933

“…Electoral control models whether the structure of an election can be modified to ensure a preferred outcome [Bartholdi et al, 1992]. Control(-to-Winner) problems for Kemeny tend to be Σ p 2 -complete [Fitzsimmons et al, 2019] (note that winner determination is already complete for parallel access to NP [Hemaspaandra et al, 2005]). In this section we provide evidence that this is also the case for Control-to-Consensus.…”

Section: Control-to-consensusmentioning

confidence: 99%

“…However, we cannot modify the approach above in a simple way, since one arc in a graph does not correspond to one voter in the corresponding election. This is also the reason that the complexity of "regular" Kemeny voter control(-to-winner) is still open [Fitzsimmons et al, 2019].…”

Section: Control-to-consensusmentioning

confidence: 99%

Kemeny Consensus Complexity

Fitzsimmons

¹

,

Hemaspaandra

²

2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition.

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“…Electoral control models whether the structure of an election can be modified to ensure a preferred outcome (Bartholdi et al, 1992). Control(-to-Winner) problems for Kemeny tend to be Σ p 2 -complete (Fitzsimmons et al, 2019) (note that winner determination is already complete for parallel access to NP (Hemaspaandra et al, 2005)). In this section we provide evidence that this is also the case for Control-to-Consensus.…”

Section: Control-to-consensusmentioning

confidence: 99%

“…Σ p 2 lower bounds are often hard to prove, in part because there are fewer known Σ p 2 -complete problems (see Schaefer and Umans (2002) for a list) and also because one needs a closer correspondence between the two problems than for NP-hardness reductions. A Σ p 2 -complete problem closely related to ours is Vertex-Cover-Member-Select (Fitzsimmons et al, 2019).…”

Section: Name: Minimum Vertex Cover Recognition Deletionmentioning

confidence: 99%

Kemeny Consensus Complexity

Fitzsimmons¹,

Hemaspaandra²

2021

Preprint

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0

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The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition.

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“…Hence, solving the resulting program of normal rules yields answer sets of the original, with possibly some added auxiliary atoms. This kind of simplification of form facilitates further processing, such as debugging [100], translation into other declarative problem representations [95], use of solving techniques to which it would be challenging to add extended rule support otherwise [47], and pursuit of increased solving performance on specific benchmark problems in Publication VI and Publication VII. In Section 3.1, a number of techniques for normalization are overviewed.…”

Section: Normalization and Visible Strong Equivalencementioning

confidence: 99%

Boosting Answer Set Optimization with Weighted Comparator Networks

Bomanson¹,

Janhunen²

2020

Theory and Practice of Logic Programming

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0

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AbstractAnswer set programming (ASP) is a paradigm for modeling knowledge-intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler ones. Normalization is a rewriting process that removes extended rule types altogether in favor of normal rules. Recently, such techniques led to optimization rewriting in ASP, where the goal is to boost answer set optimization by refactoring the optimization criteria of interest. In this paper, we present a novel, general, and effective technique for optimization rewriting based on comparator networks which are specific kinds of circuits for reordering the elements of vectors. The idea is to connect an ASP encoding of a comparator network to the literals being optimized and to redistribute the weights of these literals over the structure of the network. The encoding captures information about the weight of an answer set in auxiliary atoms in a structured way that is proven to yield exponential improvements during branch-and-bound optimization on an infinite family of example programs. The used comparator network can be tuned freely, for example, to find the best size for a given benchmark class. Experiments show accelerated optimization performance on several benchmark problems.

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Very Hard Electoral Control Problems

Cited by 5 publications

References 41 publications

Kemeny Consensus Complexity

Kemeny Consensus Complexity

Kemeny Consensus Complexity

Boosting Answer Set Optimization with Weighted Comparator Networks

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