How Hard Is It to Control an Election by Breaking Ties?
This addresses the computational difficulty of election manipulation for election designers and theorists, though it is incremental as it builds on existing complexity studies in social choice.
The paper tackles the problem of controlling election outcomes through strategic tie-breaking, proving that it can be NP-hard for a chair to compute tie-breaking strategies to ensure a given result in multi-round elections, even with a two-stage voting rule.
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.