  We investigate approval-based committee voting with incomplete information
about voters' approval preferences. 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. For a number of classic
approval-based committee voting rules including Chamberlin--Courant and
Proportional Approval Voting, we study the complexity of some fundamental
computational problems such as determining whether a given committee is a
possible or necessary winning committee and whether it possibly or necessarily
satisfies representation axioms.
