Proportionality Degree in Participatory Budgeting
This work addresses fairness in participatory budgeting for decision-makers and communities, but it is incremental as it builds on existing methods and focuses on quantitative analysis.
The paper tackles the problem of measuring proportionality in participatory budgeting by deriving tight bounds on the proportionality degree for the Method of Equal Shares and Phragmén's Sequential Rule, showing they have the same proportionality degree despite differing axiomatic guarantees, with experimental results on real-world datasets confirming the theoretical findings.
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.