# A Parameterized Perspective on Protecting Elections

## TL;DR

This paper investigates the parameterized complexity of optimal attack and defense strategies in voting systems, analyzing how attacker and defender choices affect election outcomes under various constraints.

## Contribution

It introduces a parameterized framework for analyzing attack and defense problems in voting, providing complexity results and insights into strategic election protection.

## Key findings

- Complexity results for attack and defense problems under various parameters.
- Identification of tractable and intractable cases in election protection.
- Framework for strategic analysis of voting security.

## Abstract

We study the parameterized complexity of the optimal defense and optimal attack problems in voting. In both the problems, the input is a set of voter groups (every voter group is a set of votes) and two integers $k_a$ and $k_d$ corresponding to respectively the number of voter groups the attacker can attack and the number of voter groups the defender can defend. A voter group gets removed from the election if it is attacked but not defended. In the optimal defense problem, we want to know if it is possible for the defender to commit to a strategy of defending at most $k_d$ voter groups such that, no matter which $k_a$ voter groups the attacker attacks, the outcome of the election does not change. In the optimal attack problem, we want to know if it is possible for the attacker to commit to a strategy of attacking $k_a$ voter groups such that, no matter which $k_d$ voter groups the defender defends, the outcome of the election is always different from the original (without any attack) one.