Truthful aggregation of budget proposals

We consider a participatory budgeting problem in which each voter submits a proposal for how to divide a single divisible resource (such as money or time) among several possible alternatives (such as public projects or activities) and these proposals must be aggregated into a single aggregate division. Under l(1) preferences-for which a voter's disutility is given by the l(1) distance between the aggregate division and the division he or she most prefers-the social welfare-maximizing mechanism, which minimizes the average l(1) distance between the outcome and each voter's proposal, is incentive compatible(Goel et al., 2019). However, it fails to satisfy a natural fairness notion of proportionality, placing too much weight on majority preferences. Leveraging a connection between market prices and the generalized median rules of Moulin (1980), we introduce the independent markets mechanism, which is both incentive compatible and proportional. We unify the social welfare-maximizing mechanism and the independent markets mechanism by defining a broad class of moving phantom mechanisms that includes both. We show that every moving phantom mechanism is incentive compatible. Finally, we characterize the social welfare-maximizing mechanism as the unique Pareto-optimal mechanism in this class, suggesting an inherent tradeoff between Pareto optimality and proportionality. (c) 2021 Elsevier Inc. All rights reserved.