The Possible Winner problem asks, given an election where the voters'
preferences over the candidates are specified only partially, whether a
designated candidate can be made win. Betzler and Dorn [1,2] proved a result
that is only one step away from a full dichotomy of this problem for the
important class of pure scoring rules in the case of unweighted voters and an
unbounded number of candidates: Possible Winner is NP-complete for all pure
scoring rules except plurality, veto, and the scoring rule with vector
(2,1,...,1,0), but is solvable in polynomial time for plurality and veto.