Social Welfare in Budget Aggregation
Javier Cembrano, Rupert Freeman, Ulrike Schmidt-Kraepelin, Markus Utke

TL;DR
This paper investigates proportional mechanisms for budget aggregation under $1$-utilities, introducing new mechanisms that optimize welfare and proportionality, and analyzing their theoretical properties and computational complexity.
Contribution
It introduces UtilProp, a new truthful proportional mechanism with optimal worst-case welfare ratio, and GreedyDecomp, a decomposable mechanism with strong welfare guarantees.
Findings
UtilProp achieves the optimal worst-case welfare ratio among proportional mechanisms.
UtilProp welfare-dominates all previously known single-minded proportional mechanisms.
GreedyDecomp provides a 2-approximation to the welfare-optimal decomposable mechanism.
Abstract
We study budget aggregation under -utilities, a model for collective decision making in which agents with heterogeneous preferences must allocate a public budget across a set of alternatives. Each agent reports their preferred allocation, and a mechanism selects an allocation. Early work focused on social welfare maximization, which in this setting admits truthful mechanisms, but may underrepresent minority groups, motivating the study of proportional mechanisms. However, the dominant proportionality notion, single-minded proportionality, is weak, as it only constrains outcomes when agents hold extreme preferences. To better understand proportionality and its interaction with welfare and truthfulness, we address three questions. First, how much welfare must be sacrificed to achieve proportionality? We formalize this via the price of proportionality, the best worst-case welfare…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Constraint Satisfaction and Optimization
