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

arXiv: https://arxiv.org/abs/1304.6174 · HTML: https://mlsanity.com/paper/1304.6174/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [How Hard is it to Rig a Benchmark? A Social Choice Analysis of Leaderboard Robustness](https://mlsanity.com/paper/2605.23628/) (2026)
- [On the Complexity of Winner Determination and Strategic Control in Conditional Approval Voting](https://mlsanity.com/paper/2202.01660/) (2022)

## Abstract (arXiv)

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.