Social Welfare in Budget Aggregation

A team of researchers including Javier Cembrano, Rupert Freeman, Ulrike Schmidt-Kraepelin, and Markus Utke has published a significant paper titled 'Social Welfare in Budget Aggregation' on arXiv, tackling the fundamental problem of how to fairly allocate public budgets among competing alternatives when agents have heterogeneous preferences. The work addresses the long-standing tension in collective decision-making between maximizing overall social welfare (which can disadvantage minority groups) and achieving proportional fairness (which often sacrifices efficiency). The researchers formalize this trade-off through the 'price of proportionality' metric, measuring how much welfare must be sacrificed to achieve proportional outcomes compared to the purely welfare-maximizing mechanism called Util.

The paper's key contribution is UtilProp, a novel mechanism that is both truthful (agents can't game it by misreporting preferences) and satisfies single-minded proportionality while achieving the optimal worst-case welfare ratio. The researchers prove that UtilProp welfare-dominates all previously known proportional and truthful mechanisms. Furthermore, they explore stronger fairness notions like decomposability, introducing GreedyDecomp which provides a 2-approximation to the optimal decomposable mechanism (UtilDecomp), whose computation they show to be NP-hard. This work provides both theoretical foundations and practical algorithmic solutions for improving fairness in participatory budgeting and public resource allocation systems.