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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Published in:	Information and computation Vol. 208; no. 2; pp. 165 - 177
Main Authors:	Betzler, Nadja, Guo, Jiong, Niedermeier, Rolf
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 01.02.2010 Elsevier
Subjects:	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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Abstract	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.
AbstractList	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.
Author	Niedermeier, Rolf Guo, Jiong Betzler, Nadja
Author_xml	– sequence: 1 givenname: Nadja surname: Betzler fullname: Betzler, Nadja email: nadja.betzler@uni-jena.de – sequence: 2 givenname: Jiong surname: Guo fullname: Guo, Jiong email: jiong.guo@uni-jena.de – sequence: 3 givenname: Rolf surname: Niedermeier fullname: Niedermeier, Rolf email: rolf.niedermeier@uni-jena.de
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Keywords	Winner determination Computational social choice W-completeness Fixed-parameter tractability Voting systems Costs Computer theory Algorithm Computational complexity Switching Voting Completeness NP complete problem
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Snippet	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...
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SubjectTerms	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
Title	Parameterized computational complexity of Dodgson and Young elections
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