  In the committee voting setting, a subset of $k$ alternatives is selected
based on the preferences of voters. In this paper, our goal is to efficiently
compute ex-ante fair probability distributions (or lotteries) over committees.
Since it is not known whether a lottery satisfying the desirable fairness
property of fractional core is polynomial-time computable, we introduce a new
axiom called group resource proportionality (GRP), which strengthens other
fairness notions in the literature. We characterize our fairness axiom by a
correspondence with max flows on a network formulation of committee voting.
Using the connection to flow networks revealed by this characterization, we
then introduce voting rules which achieve fairness in conjunction with other
desirable properties. The redistributive utilitarian rule satisfies ex-ante
efficiency in addition to our fairness axiom. We also give a voting rule which
maximizes social welfare subject to fairness by reducing to a minimum-cost
maximum-flow problem. Lastly, we show our fairness property can be obtained in
tandem with strong ex-post fairness properties -- an approach known as
best-of-both-worlds fairness. We strengthen existing best-or-both-worlds
fairness results in committee voting and resolve an open question posed by Aziz
et al. (2023). These findings follow from an auxiliary result which may prove
useful in obtaining best-of-both-worlds type results in future research on
committee voting.
