  Usually a voting rule requires agents to give their preferences as linear
orders. However, in some cases it is impractical for an agent to give a linear
order over all the alternatives. It has been suggested to let agents submit
partial orders instead. Then, given a voting rule, a profile of partial orders,
and an alternative (candidate) c, two important questions arise: first, is it
still possible for c to win, and second, is c guaranteed to win? These are the
possible winner and necessary winner problems, respectively. Each of these two
problems is further divided into two sub-problems: determining whether c is a
unique winner (that is, c is the only winner), or determining whether c is a
co-winner (that is, c is in the set of winners). We consider the setting where
the number of alternatives is unbounded and the votes are unweighted. We
completely characterize the complexity of possible/necessary winner problems
for the following common voting rules: a class of positional scoring rules
(including Borda), Copeland, maximin, Bucklin, ranked pairs, voting trees, and
plurality with runoff.
