Complexity of Control by Partition of Voters and of Voter Groups in Veto and Other Scoring Protocols

In order to model maliciously resizing election districts (a.k.a. gerrymandering), Bartholdi et al. [2] introduced control by partition of voters, which means that an election chair can influence the outcome of an election to her advantage by partitioning the voters such that two first-round subelections are created whose winners will take part in a final runoff. Control by partition of voter groups, due to Erdélyi et al. [10], refers to the same model with the additional constraint that a partition of voters into groups is given beforehand, which the chair's control action must respect: either all voters of a group take part in one of the two first-round subelections, or none of them does. Maushagen and Rothe [25] recently classified some problems of control by partition of either voters or candidates for veto elections in terms of their computational complexity, leaving some other problems open. We solve all these remaining cases. In addition, we generalize a result of Erdélyi et al. [10] for constructive control by partition of voter groups from plurality elections to all nontrivial pure scoring protocols by showing NP-hardness, and we also obtain the analogous result for its destructive variant.