  We investigate approval-based committee voting with incomplete information
about the approval preferences of voters. We consider several models of
incompleteness where each voter partitions the set of candidates into approved,
disapproved, and unknown candidates, possibly with ordinal preference
constraints among candidates in the latter category. This captures scenarios
where voters have not evaluated all candidates and/or it is unknown where
voters draw the threshold between approved and disapproved candidates. We study
the complexity of some fundamental computational problems for a number of
classic approval-based committee voting rules including Proportional Approval
Voting and Chamberlin--Courant. These problems include that of determining
whether a given set of candidates is a possible or necessary winning committee
and whether it forms a committee that possibly or necessarily satisfies
representation axioms. We also consider the problem whether a given candidate
is possibly or necessarily a member of the winning committee.
