Proportionally Representative Participatory Budgeting with Ordinal Preferences

TL;DR

This paper introduces proportional representation axioms for participatory budgeting with ordinal preferences, proposes new solution concepts, and demonstrates polynomial-time algorithms satisfying these fairness criteria.

Contribution

It formalizes proportional representation in PB with ordinal preferences, introduces the Inclusion PSC (IPSC) concept, and shows polynomial algorithms can satisfy these fairness axioms.

Findings

Proposed proportional representation axioms for PB with ordinal preferences.

Introduced the Inclusion PSC (IPSC) solution concept for approval-based multi-winner voting.

Developed polynomial-time algorithms satisfying EJR and IPSC axioms.

Abstract

Participatory budgeting (PB) is a democratic paradigm whereby voters decide on a set of projects to fund with a limited budget. We consider PB in a setting where voters report ordinal preferences over projects and have (possibly) asymmetric weights. We propose proportional representation axioms and clarify how they fit into other preference aggregation settings, such as multi-winner voting and approval-based multi-winner voting. As a result of our study, we also discover a new solution concept for approval-based multi-winner voting, which we call Inclusion PSC (IPSC). IPSC is stronger than proportional justified representation (PJR), incomparable to extended justified representation (EJR), and yet compatible with EJR. The well-studied Proportional Approval Voting (PAV) rule produces a committee that satisfies both EJR and IPSC; however, both these axioms can also be satisfied by an algorithm that runs in polynomial-time.