  An important question in elections is the determine whether a candidate can
be a winner when some votes are absent. We study this determining winner with
the absent votes (WAV) problem when the votes are top-truncated. We show that
the WAV problem is NP-complete for the single transferable vote, Maximin, and
Copeland, and propose a special case of positional scoring rule such that the
problem can be computed in polynomial time. Our results in top-truncated
rankings differ from the results in full rankings as their hardness results
still hold when the number of candidates or the number of missing votes are
bounded, while we show that the problem can be solved in polynomial time in
either case.
