Multiwinner Elections - model with Issues

We study a model of Multiwinner Elections with Issues, in which we assume that an instance consists of a set of individuals (voters and candidates), desired committee size k and p Issues, which will be voted on by the winning committee. The goal is to select a winning committee such that decision made by them (majority decision) maximizes the utility of voters. We assume that each individual is represented as binary vector such that i-th position indicates preference of the individual over i-th Issue. What's more, we also assume that instead of preferences of the individuals over Issues we know only the preferences of voters over candidates, which are inducted by the preferences over Issues (i.e. the more preferences voter and candidate have in common, the more this candidate is prefered by the voter). Once we have vectors of voters' preferences over candidates we can use different ordinal voting rules to select the winning committee. Our aim is to compare ordinal voting rules (such as SNTV, STV, k-Borda, Chamberlin-Courant, Monroe, Borda-PAV) with each other in the considered model and obtain the possible losses of utility, when the ordinal voting rule has to be applied.