  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 analyse whether a
representative committee exists and also examine the complexity of computing
and verifying such a committee.
