  The Possible Winner problem asks, given an election where the voters'
preferences over the candidates are specified only partially, whether a
designated candidate can become a winner by suitably extending all the votes.
Betzler and Dorn [1] 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. We take the final step to a full dichotomy by showing
that Possible Winner is NP-complete also for the scoring rule with vector
(2,1,...,1,0).
