Price of Fairness in Budget Division for Egalitarian Social Welfare

TL;DR

This paper analyzes the efficiency loss caused by fairness constraints in participatory budgeting, providing bounds on the price of fairness and evaluating aggregation rules' performance.

Contribution

It introduces bounds on the price of fairness and assesses the efficiency guarantees of various aggregation rules in budget division.

Findings

Tight bounds for the price of fairness are established.

Performance guarantees for aggregation rules are derived.

Efficiency loss due to fairness constraints is quantitatively characterized.

Abstract

We study a participatory budgeting problem of aggregating the preferences of agents and dividing a budget over the projects. A budget division solution is a probability distribution over the projects. The main purpose of our study concerns the comparison between the system optimum solution and a fair solution. We are interested in assessing the quality of fair solutions, i.e., in measuring the system efficiency loss under a fair allocation compared to the one that maximizes (egalitarian) social welfare. This indicator is called the price of fairness. We are also interested in the performance of several aggregation rules. Asymptotically tight bounds are provided both for the price of fairness and the efficiency guarantee of aggregation rules.