Parameterized computational complexity of Dodgson and Young elections

We show that the two NP-complete problems of Dodgson Score and Young Score have differing computational complexities when the winner is close to being a Condorcet winner. On the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a m...

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Vydáno v:Information and computation Ročník 208; číslo 2; s. 165 - 177
Hlavní autoři: Betzler, Nadja, Guo, Jiong, Niedermeier, Rolf
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Inc 01.02.2010
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computational social choice
Computer science; control theory; systems
Exact sciences and technology
Fixed-parameter tractability
Miscellaneous
Theoretical computing
Voting systems
W-completeness
Winner determination
Winner determination
Computational social choice
W-completeness
Fixed-parameter tractability
Voting systems
Costs
Computer theory
Algorithm
Computational complexity
Switching
Voting
Completeness
NP complete problem
ISSN:0890-5401, 1090-2651
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Popis
Shrnutí:We show that the two NP-complete problems of Dodgson Score and Young Score have differing computational complexities when the winner is close to being a Condorcet winner. On the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-completeness results depending on the cost model for switching ties.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2009.10.001