Sub-committee Approval Voting and Generalised Justified Representation Axioms

TL;DR

This paper introduces a general model called Sub-Committee Voting that unifies various social choice settings and extends justified representation axioms to approval-based sub-committee voting, analyzing their properties, existence, and computational complexity.

Contribution

It proposes new axioms for approval-based sub-committee voting within a unified model and studies their properties, existence, and computational aspects.

Findings

Certain axioms guarantee the existence of representative committees.

Computational complexity results for verifying and computing committees vary by axiom.

The model generalizes multiple social choice scenarios.

Abstract

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.