Challenges to complexity shields that are supposed to protect elections against manipulation and control: a survey

In the context of voting, manipulation and control refer to attempts to influence the outcome of elections by either setting some of the votes strategically (i.e., by reporting untruthful preferences) or by altering the structure of elections via adding, deleting, or partitioning either candidates o...

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Bibliographic Details
Published in:Annals of mathematics and artificial intelligence Vol. 68; no. 1-3; pp. 161 - 193
Main Authors: Rothe, Jörg, Schend, Lena
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.07.2013
Springer Nature B.V
Subjects:
Artificial Intelligence
Complex Systems
Complexity
Computer Science
Control systems
Elections
Expert systems
Hardness
Mathematics
Principles
Shields
Voting
Voting systems
Voting theory
68T99
Computational social choice
Control
Manipulation
68Q17
ISSN:1012-2443, 1573-7470
Online Access:Get full text
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Summary:In the context of voting, manipulation and control refer to attempts to influence the outcome of elections by either setting some of the votes strategically (i.e., by reporting untruthful preferences) or by altering the structure of elections via adding, deleting, or partitioning either candidates or voters. Since by the celebrated Gibbard–Satterthwaite theorem (and other results expanding its scope) all reasonable voting systems are manipulable in principle and since many voting systems are in principle susceptible to many control types modeling natural control scenarios, much work has been done to use computational complexity as a shield to protect elections against manipulation and control. However, most of this work has merely yielded NP-hardness results, showing that certain voting systems resist certain types of manipulation or control only in the worst case. Various approaches, including studies of the typical case (where votes are given according to some natural distribution), pose serious challenges to such worst-case complexity results and might allow successful manipulation or control attempts, despite the NP-hardness of the corresponding problems. We survey and discuss some recent results on these challenges to complexity results for manipulation and control, including typical-case analyses and experiments, fixed-parameter tractability, domain restrictions (single-peakedness), and approximability.
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-013-9359-5