  The Borda voting rule is a positional scoring rule for $z$ candidates such
that in each vote, the first candidate receives $z-1$ points, the second $z-2$
points and so on. The winner in the Borda rule is the candidate with highest
total score. We study the manipulation problem of the Borda rule in a setting
with two non-manipulators while one of the non-manipulator's vote is weighted.
We demonstrate a sharp contrast on computational complexity depending on the
weight of the non-manipulator: the problem is NP-hard when the weight is larger
than $1$ while there exists an efficient algorithm to find a manipulation when
the weight is at most $1$.
