When are elections with few candidates hard to manipulate?
Journal of the ACM (JACM)
Average-case tractability of manipulation in voting via the fraction of manipulators
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Generalized scoring rules and the frequency of coalitional manipulability
Proceedings of the 9th ACM conference on Electronic commerce
Algorithms for the coalitional manipulation problem
Artificial Intelligence
How hard is bribery in elections?
Journal of Artificial Intelligence Research
Preference functions that score rankings and maximum likelihood estimation
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Finite local consistency characterizes generalized scoring rules
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Complexity of unweighted coalitional manipulation under some common voting rules
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Risk-limiting postelection audits: conservative P-values from common probability inequalities
IEEE Transactions on Information Forensics and Security - Special issue on electronic voting
Using complexity to protect elections
Communications of the ACM
Security analysis of India's electronic voting machines
Proceedings of the 17th ACM conference on Computer and communications security
Super-simple simultaneous single-ballot risk-limiting audits
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Estimating the margin of victory for instant-runoff voting
EVT/WOTE'11 Proceedings of the 2011 conference on Electronic voting technology/workshop on trustworthy elections
Computing the margin of victory in IRV elections
EVT/WOTE'11 Proceedings of the 2011 conference on Electronic voting technology/workshop on trustworthy elections
How hard is it to control an election?
Mathematical and Computer Modelling: An International Journal
A Bayesian method for auditing elections
EVT/WOTE'12 Proceedings of the 2012 international conference on Electronic Voting Technology/Workshop on Trustworthy Elections
On coalitions and stable winners in plurality
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
The complexity of losing voters
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
On elections with robust winners
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Schulze and ranked-pairs voting are fixed-parameter tractable to bribe, manipulate, and control
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Generalized scoring rules: a framework that reconciles Borda and Condorcet
ACM SIGecom Exchanges
How to change a group's collective decision?
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
The complexity of manipulative attacks in nearly single-peaked electorates
Artificial Intelligence
Bribery in voting with CP-nets
Annals of Mathematics and Artificial Intelligence
A smooth transition from powerlessness to absolute power
Journal of Artificial Intelligence Research
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The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines. In this paper, we investigate the computational complexity and (in)approximability of computing the margin of victory for various voting rules, including approval voting, all positional scoring rules (which include Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also prove a dichotomy theorem, which states that for all continuous generalized scoring rules, including all voting rules studied in this paper, either with high probability the margin of victory is Θ(√n), or with high probability the margin of victory is Θ(n), where n is the number of voters. Most of our results are quite positive, suggesting that the margin of victory can be efficiently computed. This sheds some light on designing efficient post-election audits for voting rules beyond the plurality rule.