Anyone but Him: The Complexity of Precluding an Alternative
Abstract
Preference aggregation in a multiagent setting is a central issue in both human and computer contexts. In this paper, we study in terms of complexity the vulnerability of preference aggregation to destructive control. That is, we study the ability of an election's chair to, through such mechanisms as voter/candidate addition/suppression/partition, ensure that a particular candidate (equivalently, alternative) does not win. And we study the extent to which election systems can make it impossible, or computationally costly (NP-complete), for the chair to execute such control. Among the systems we study--plurality, Condorcet, and approval voting--we find cases where systems immune or computationally resistant to a chair choosing the winner nonetheless are vulnerable to the chair blocking a victory. Beyond that, we see that among our studied systems no one system offers the best protection against destructive control. Rather, the choice of a preference aggregation system will depend closely on which types of control one wishes to be protected against. We also find concrete cases where the complexity of or susceptibility to control varies dramatically based on the choice among natural tie-handling rules.
Keywords
Cite
@article{arxiv.cs/0507027,
title = {Anyone but Him: The Complexity of Precluding an Alternative},
author = {Edith Hemaspaandra and Lane A. Hemaspaandra and Joerg Rothe},
journal= {arXiv preprint arXiv:cs/0507027},
year = {2026}
}
Comments
This revision--the March 2026 Version 5--is identical to the March 2006 Version 4 except in providing, as Appendix A, a correction to the second half of the proof of Theorem 4.21 as it appears in both Version 4 and the AIJ journal version; this proof also replaces the analogous proof part of Theorem 6 of the AAAI version