Control studies attempts to set the outcome of elections through the addition, deletion, or partition of voters or candidates. The set of benchmark control types was largely set in the seminal 1992 paper by Bartholdi, Tovey, and Trick that introduced
control, and there now is a large literature studying how many of the benchmark types various election systems are vulnerable to, i.e., have polynomial-time attack algorithms for. However, although the longstanding benchmark models of addition and deletion model relatively well the real-world settings that inspire them, the longstanding benchmark models of partition model settings that are arguably quite distant from those they seek to capture. In this paper, we introduce--and for some important cases analyze the complexity of--new partition models that seek to better capture many real-world partition settings. In particular, in many partition settings one wants the two parts of the partition to be of (almost) equal size, or is partitioning into more than two parts, or has groups of actors who must be placed in the same part of the partition. Our hope is that having these new partition types will allow studies of control attacks to include such models that more realistically capture many settings.
We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomial-time algorithm. We also study some features of probability weight of cor
rectness with respect to generalizations of Procaccia and Rosenscheins junta distributions [PR07b].
