Committee Voting with Incomplete Approvals

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.