1 research outputs found
Manipulation is Harder with Incomplete Votes
The Coalitional Manipulation (CM) problem has been studied extensively in the
literature for many voting rules. The CM problem, however, has been studied
only in the complete information setting, that is, when the manipulators know
the votes of the non-manipulators. A more realistic scenario is an incomplete
information setting where the manipulators do not know the exact votes of the
non- manipulators but may have some partial knowledge of the votes. In this
paper, we study a setting where the manipulators know a partial order for each
voter that is consistent with the vote of that voter. In this setting, we
introduce and study two natural computational problems - (1) Weak Manipulation
(WM) problem where the manipulators wish to vote in a way that makes their
preferred candidate win in at least one extension of the partial votes of the
non-manipulators; (2) Strong Manipulation (SM) problem where the manipulators
wish to vote in a way that makes their preferred candidate win in all possible
extensions of the partial votes of the non-manipulators. We study the
computational complexity of the WM and the SM problems for commonly used voting
rules such as plurality, veto, k-approval, k-veto, maximin, Copeland, and
Bucklin. Our key finding is that, barring a few exceptions, manipulation
becomes a significantly harder problem in the setting of incomplete votes.Comment: 15 page