We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of @math items that maximize the total derived utility of all the agents (i.e., in our example we are to pick @math movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.
Given a set of voters V, a set of candidates C, and voters' preferences over the candidates, multiwinner voting rules output a fixed-size subset of candidates committee. Under the Chamberlin---Courant multiwinner voting rule, one fixes a scoring vector of length |C|, and each voter's 'utility' for a given committee is defined to be the score that she assigns to her most preferred candidate in that committee; the goal is then to find a committee that maximizes the joint utility of all voters. The joint utility is typically identified either with the sum of all voters' utilities or with the utility of the least satisfied voter, resulting in, respectively, the utilitarian and the egalitarian variant of the Chamberlin---Courant's rule. For both of these cases, the problem of computing an optimal committee is NP-hard for general preferences, but becomes polynomial-time solvable if voters' preferences are single-peaked or single-crossing. In this paper, we propose a family of multiwinner voting rules that are based on the concept of ordered weighted average OWA and smoothly interpolate between the egalitarian and the utilitarian variants of the Chamberlin---Courant rule. We show that under moderate constraints on the weight vector we can recover many of the algorithmic results known for the egalitarian and the utilitarian version of Chamberlin---Courant's rule in this more general setting.