Proportionality Degree in Participatory Budgeting

TL;DR

This paper studies the proportionality degree in participatory budgeting, analyzing two popular methods, deriving tight bounds, and validating findings through extensive experiments on real-world data.

Contribution

It provides the first theoretical bounds on the proportionality degree of MES and Phragmen's rule, showing they have similar quantitative guarantees despite different axioms.

Findings

Both rules have similar proportionality degrees.

Experimental results align with theoretical bounds.

Insights into rule comparisons from real-world data.

Abstract

We initiate the study of the proportionality degree for participatory budgeting, with a particular focus on two popular methods: the Method of Equal Shares (MES) and Phragmen's Sequential Rule. Among other results, we derive tight bounds (up to small constant factors) on the proportionality degree of these two rules, which showcase that, despite MES satisfying stronger axiomatic guarantees, the two rules have the same proportionality degree from a quantitative perspective. We complement our theoretical findings with an extensive experimental evaluation on real-world participatory budgeting datasets, the results of which closely mirror those of our developed theory. Our experiments also provide more insights into the comparisons between the rules.