How Hard Is It to Control an Election by Breaking Ties?

TL;DR

This paper investigates the computational difficulty of controlling election outcomes through strategic tie-breaking, revealing NP-hardness in multi-round elections and the impact of tie-breaking functions on control opportunities.

Contribution

It demonstrates that controlling election results via tie-breaking is NP-hard in multi-round settings and highlights how tie-breaking functions influence control complexity.

Findings

NP-hardness in multi-round elections for tie-breaking control

Tie-breaking functions can increase control opportunities

Controlling elections by tie-breaking remains complex even with simple rules

Abstract

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the chair of the election is only asked to break ties to choose between one of the co-winners, the problem is trivially easy. However, in multi-round elections, we prove that it can be NP-hard for the chair to compute how to break ties to ensure a given result. Additionally, we show that the form of the tie-breaking function can increase the opportunities for control. Indeed, we prove that it can be NP-hard to control an election by breaking ties even with a two-stage voting rule.