It'd almost certainly seem interesting to see whether one might manage to crosspollinate the above paper with this 'recent' generalization result from parameterized computational social choice theory:<p><a href="https://arxiv.org/abs/1711.06030" rel="nofollow">https://arxiv.org/abs/1711.06030</a><p>(Published version, closed access: <a href="https://dl.acm.org/citation.cfm?id=3278739" rel="nofollow">https://dl.acm.org/citation.cfm?id=3278739</a>)<p>Aziz, Haris; Lee, Barton E. – Sub-committee Approval Voting and Generalised Justified Representation Axioms (2017/2018)<p>Abstract:<p>"Social choice is replete with various settings including single-winner voting, multi-winner voting, probabilistic voting, multiple referenda, and public decision making. We study a general model of social choice called sub-committee voting (SCV) that simultaneously generalizes these settings. We then focus on sub-committee voting with approvals and propose extensions of the justified representation axioms that have been considered for proportional representation in approval-based committee voting. We study the properties and relations of these axioms. For each of the axioms, we analyze whether a representative committee exists and also examine the complexity of computing and verifying such a committee."<p>Citations: <a href="https://scholar.google.com/scholar?cites=5804298394619698922" rel="nofollow">https://scholar.google.com/scholar?cites=5804298394619698922</a><p>And then, perhaps, <i>that theorem of infamity by that dude who might have gone by—some name(, like, uh, )—'Aumann'</i>