Anyone but Him: The Complexity of Precluding an Alternative

TL;DR

This paper analyzes the computational complexity of preventing an election chair from manipulating outcomes through destructive control methods across various voting systems, revealing no single system offers complete protection.

Contribution

It provides a detailed complexity analysis of destructive control in multiple voting systems, highlighting vulnerabilities and the impact of tie-handling rules.

Findings

Some systems are resistant or immune to certain control types.

Vulnerability varies significantly with tie-handling rules.

No single voting system offers comprehensive protection.

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.