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 $\ell_1$ preferences -- for which a voter's disutility is given by the $\ell_1$ distance between the aggregate division and the division he or she most prefers -- the social welfare-maximizing mechanism, which minimizes the average $\ell_1$ distance between the outcome and each voter's proposal, is incentive compatible (Goel et al. 2016). However, it fails to satisfy the 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.
翻译:我们考虑一个参与性预算编制问题,即每个选民就如何在几种可能的替代方案(如公共项目或活动)之间分配单一的可变资源(如金钱或时间)提出建议,这些提议必须合并成一个单一的总分配。在美元1美元的优惠下,选民的不能利用是由总分配与他或她最喜欢的划分之间的1美元距离给予的。社会福利-最大化机制将结果与每个选民提议之间的平均1美元差幅最小化,这是相互兼容的奖励办法(Goel等人,2016年)。然而,它未能满足自然公平的相称性概念,过分强调多数偏好。在市场价格与Moulin(1980年)的通用中位规则之间建立联系,我们引入独立的市场机制,该机制既是奖励办法的兼容性,也是相称的。我们把社会福利-最大化机制和独立市场机制统一起来,方法是确定一种包括两者在内的广泛的移动幻象机制。我们表明,每个移动的幻象机制都是相互兼容的。最后,我们把这种内在的贸易机制定性为一种独特的标准。