Efficiency in multiwinner voting is most naturally captured by Pareto-optimality (PO), yet this notion is computationally and structurally difficult to handle. We therefore study fractional Pareto-optimality (fPO), under which a committee may not be dominated even by a fractional committee, i.e., any convex combination of committees. fPO turns out to be a natural refinement of PO as it retains exactly those Pareto-optimal committees whose efficiency is robust under uniform cloning of candidates. Furthermore, fPO committees are guaranteed to exist and have strong structural properties. We present a characterization of fPO in terms of weighted utilitarian welfare maximization, which yields a polynomial-time algorithm for verifying fPO and shows that the set of fPO committees satisfies committee monotonicity and is connected under single-candidate swaps. Analyzing welfarist rules through the lens of fPO, we further uncover an incompatibility between fPO and equality-oriented objectives. Most notably, we show that proportional approval voting (PAV) violates fPO in the approval setting. We close by pinpointing preference domains, including various one-dimensional ones, on which PO and fPO collapse into one notion.
We resolve the central open question in the theory of approval-based committee elections: we prove that the core is always non-empty. This means that there always exists a committee for which no coalition of voters can deviate to an alternative committee of proportional size that every member strictly prefers. This property was introduced by Aziz et al. (2017) to capture proportional representation and coalitional stability, but no known algorithm achieved it except up to a constant approximation factor or in special cases. Our approach begins by strengthening the core to core+, which requires the committee to be robust even to fractional deviations. Using LP duality, this property can equivalently be defined in terms of a payment-based certificate under which no losing candidate gathers too much support. We then define a voting rule that chooses a committee admitting a certificate that maximizes a novel harmonic entropy objective function, which rewards balanced payment distributions. We show that the payment system associated with an optimal committee certifies that the committee satisfies core+, establishing existence. The same is true for local optima, which allows us to design a polynomial-time algorithm computing a core+ committee.