We investigate the problem of coalitional manipulation in elections, which is known to be hard in a variety of voting rules. We put forward efficient algorithms for the problem in Borda, Maximin and Plurality with Runoff, and analyze their windows of error. Specifically, given an instance on which an algorithm fails, we bound the additional power the manipulators need in order to succeed. We finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation.
Bibliographical noteFunding Information:
The authors would like to thank Vincent Conitzer for excellent comments on a draft of this paper, and in particular for pointing out the alternative 2-approximation algorithm for Maximin given in Appendix B. The authors also thank the anonymous AIJ reviewers for insightful comments. This work was partially supported by Israel Science Foundation grant #898/05.
* Corresponding author. E-mail addresses: email@example.com (M. Zuckerman), firstname.lastname@example.org (A.D. Procaccia), email@example.com (J.S. Rosenschein). 1 The author thanks Noam Nisan for a generous grant which supported this work. 2 The author was supported in this work by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.
- Computational complexity
- Computational social choice