One of the key topics of computational social choice is electoral control, which models certain ways of how an election chair can seek to influence the outcome of elections via structural changes such as adding, deleting, or partitioning either candidates or voters. Faliszewski and Rothe [13] have surveyed the rich literature on control, giving an overview of previous results on the complexity of the associated problems for the most important voting rules. Among those, only a few results were known for two quite prominent voting rules: Borda Count and maximin voting (a.k.a. the Simpson–Kramer rule). Neveling and Rothe [26, 25] recently settled the remaining open cases for Borda. In this paper, we solve all remaining open cases for the complexity of control in maximin elections all of which concern control by partition of either candidates or voters.

Control by partition refers to situations where an election chair seeks to influence the outcome of an election by partitioning either the candidates or the voters into two groups, thus creating two first-round subelections that determine who will take part in a final round. The model of partition-of-voters control attacks is remotely related to “gerrymandering” (maliciously resizing election districts). While the complexity of control by partition (and other control actions) has been studied thoroughly for many voting systems, there are no such results known for the important veto and maximin voting systems. We settle the complexity of control by partition for veto in a broad variety of models and for maximin with respect to destructive control by partition of candidates. We also observe that a reduction from the literature [8] showing the parameterized complexity of control by adding candidates to plurality elections, parameterized by the number of voters, is technically flawed by giving a counterexample, and we show how this reduction can be fixed.