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 determining whether a given set of candidates is a possible or necessary winning committee and whether a given candidate is possibly or necessarily a member of the winning committee. We also consider proportional representation axioms and the problem of deciding whether a given committee is possibly or necessarily representative.

We consider spatial voting where candidates are located in the Euclidean d-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location of voters' ideal points is incomplete: for each dimension, we are given an interval of possible values. We study the computational complexity of finding the possible and necessary winners for positional scoring rules. Our results show that we retain tractable cases of the classic model where voters have partial-order preferences. Moreover, we show that there are positional scoring rules under which the possible-winner problem is intractable for partial orders, but tractable in the one-dimensional spatial setting. We also consider approval voting in this setting. We show that for up to two dimensions, the necessary-winner problem is tractable, while the possible-winner problem is hard for any number of dimensions.

A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the context of noisy operations such as missing data imputation, where we automatically fill in missing values, column prediction, where we predict unknown attributes, and database cleaning (and repairing), where we replace the original values due to detected errors or violation of integrity constraints. We study the computational complexity of problems that regard the selection of cell values in the presence of integrity constraints. More precisely, we focus on functional dependencies and study three problems: (1) deciding whether the constraints can be satisfied by any choice of values, (2) finding a most probable such choice, and (3) calculating the probability of satisfying the constraints. The data complexity of these problems is determined by the combination of the set of functional dependencies and the collection of uncertain attributes. We give full classifications into tractable and intractable complexities for several classes of constraints, including a single dependency, matching constraints, and unary functional dependencies.

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.