We consider the problem of protecting and manipulating elections by recounting and changing ballots, respectively. Our setting involves a plurality-based election held across multiple districts, and the problem formulations are based on the model proposed recently by~[Elkind et al, IJCAI 2019]. It turns out that both of the manipulation and protection problems are NP-complete even in fairly simple settings. We study these problems from a parameterized perspective with the goal of establishing a more detailed complexity landscape. The parameters we consider include the number of voters, and the budgets of the attacker and the defender. While we observe fixed-parameter tractability when parameterizing by number of voters, our main contribution is a demonstration of parameterized hardness when working with the budgets of the attacker and the defender.
@article{arxiv.2005.03176,
title = {A Parameterized Perspective on Attacking and Defending Elections},
author = {Kishen N. Gowda and Neeldhara Misra and Vraj Patel},
journal= {arXiv preprint arXiv:2005.03176},
year = {2020}
}