  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.
