Exact Complexity of the Winner Problem for Young Elections

Rothe, Jörg; Spakowski, Holger; Vogel, Jörg

doi:10.1007/s00224-002-1093-z

Cited by 87 publications

(94 citation statements)

References 21 publications

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“…For the remaining rules the computational complexity is much higher: Deciding whether a candidate is a winner was shown to be Θ P 2 -complete for Dodgson [19], Young [28] as well as Kemeny [20]. Recall that the class Θ P 2 contains all problems that can be decided in polynomial time by a deterministic Turing machine using O(log n) calls to an NP-oracle, where n is the input size.…”

Section: Voting Theorymentioning

confidence: 99%

Democratix: A Declarative Approach to Winner Determination

Charwat

Pfandler

2015

Algorithmic Decision Theory

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Computing the winners of an election is an important subtask in voting and preference aggregation. The declarative nature of answer-set programming (ASP) and the performance of state-of-the-art solvers render ASP very well-suited to tackle this problem. In this work we present a novel, reduction-based approach for a variety of voting rules, ranging from tractable cases to problems harder than NP. In addition, we discuss how encodings of voting rules can be optimized and combined in our approach. The encoded voting rules are put together in the extensible tool DEMOCRATIX, which handles the computation of the winners and is also available as a web application.To learn more about the capabilities and limits of the approach, the encodings are evaluated thoroughly on real-world data as well as on random instances.

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Section: Voting Theorymentioning

confidence: 99%

Democratix: A Declarative Approach to Winner Determination

Charwat

Pfandler

2015

Algorithmic Decision Theory

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“…For example, a rule such as Borda requires nothing more than adding up the scores of the alternatives. However, this is not the case for all voting rules: some of them are in fact NPhard to execute (Bartholdi, Tovey, & Trick 1989b;Hemaspaandra, Hemaspaandra, & Rothe 1997;Cohen, Schapire, & Singer 1999;Dwork et al 2001;Rothe, Spakowski, & Vogel 2003;Ailon, Charikar, & Newman 2005;Alon 2006;Conitzer 2006;Procaccia, Rosenschein, & Zohar 2007;Brandt, Fischer, & Harrenstein 2007). As an example, let us take the Slater rule, which requires finding a ranking that is inconsistent with the outcomes of as few pairwise elections as possible.…”

Section: Votingmentioning

confidence: 99%

Comparing multiagent systems research in combinatorial auctions and voting

Conitzer

2010

Ann Math Artif Intell

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In a combinatorial auction, a set of resources is for sale, and agents can bid on subsets of these resources. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this paper is to give a convenient side-by-side comparison that will clarify the relation between the domains, and serve as a guide to future research.

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“…In Young's system, whoever can be made a Condorcet winner by removing the smallest number of voters wins. Rothe, Spakowski, and Vogel [RSV03] proved that the winner problem for Young elections is Θ p 2 -complete, via a reduction from the problem maximum-set-packing-compare. Kemeny's winners are defined via the notion of a "Kemeny consensus."…”

Section: Dodgson-winnermentioning

confidence: 99%