Sub-committee Approval Voting and Generalised Justified Representation Axioms
This work addresses proportional representation in social choice settings, but it is incremental as it extends existing axioms to a more general model.
The paper tackles the problem of extending justified representation axioms to a general model of sub-committee voting with approvals, analyzing properties, existence, and computational complexity for representative committees.
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.