  Understanding when and how computational complexity can be used to protect
elections against different manipulative actions has been a highly active
research area over the past two decades. A recent body of work, however, has
shown that many of the NP-hardness shields, previously obtained, vanish when
the electorate has single-peaked or nearly single-peaked preferences. In light
of these results, we investigate whether it is possible to reimpose NP-hardness
shields for such electorates by allowing the voters to specify partial
preferences instead of insisting they cast complete ballots. In particular, we
show that in single-peaked and nearly single-peaked electorates, if voters are
allowed to submit top-truncated ballots, then the complexity of manipulation
and bribery for many voting rules increases from being in P to being
NP-complete.
