  In a representative democracy, the electoral process involves partitioning
geographical space into districts which each elect a single representative.
These representatives craft and vote on legislation, incentivizing political
parties to win as many districts as possible (ideally a plurality).
Gerrymandering is the process by which district boundaries are manipulated to
the advantage of a desired candidate or party. We study the parameterized
complexity of Gerrymandering, a graph problem (as opposed to Euclidean space)
formalized by Cohen-Zemach et al. (AAMAS 2018) and Ito et al. (AAMAS 2019)
where districts partition vertices into connected subgraphs. We prove that Unit
Weight Gerrymandering is W[2]-hard on trees (even when the depth is two) with
respect to the number of districts $k$. Moreover, we show that Unit Weight
Gerrymandering remains W[2]-hard in trees with $\ell$ leaves with respect to
the combined parameter $k+\ell$. In contrast, Gupta et al. (SAGT 2021) give an
FPT algorithm for Gerrymandering on paths with respect to $k$. To complement
our results and fill this gap, we provide an algorithm to solve Gerrymandering
that is FPT in $k$ when $\ell$ is a fixed constant.
