The Possible Winner Problem with Uncertain Weights Revisited

Abstract

Baumeister et al. [8] introduced the possible winner with uncertain weights problem which, given a weighted election with the weights of some voters as yet unspecified, asks whether one can assign weights to these voters such that a distinguished candidate wins. Solving all questions they specifically left open for nonnegative integer weights, we show that two variants of this problem for 3-approval and four variants for plurality with runoff can be solved efficiently. In addition, we study variants of this problem for Borda, k-veto, and veto with runoff in terms of their computational complexity. Finally, we also prove that the problem of constructive control by adding voters in succinct representation belongs to P for plurality with runoff and veto with runoff.