Welfare vs. Representation in Participatory Budgeting

Abstract: Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of members of the community. Different rules have been used to aggregate participants' votes. Past research has studied the trade-off between notions of social welfare and fairness in the multi-winner setting (a special case of participatory budgeting with identical project costs) by Lackner and Skowron (2020). But there is little understanding of this trade-off in the more general PB setting. This paper provides a theoretical and empirical study of the worst-case guarantees of several common rules to better understand the trade-off between social welfare, representation. We show that many of the guarantees from the multi-winner setting do not generalize to the PB setting, and that the introduction of costs leads to substantially worse guarantees, thereby exacerbating the welfare-representation trade-off. We extend our theoretical analysis to studying how the requirement of proportionality over voting rules affects this trade-off. We further study how the requirement of proportionality over voting rules effects the guarantees on social welfare and representation. We study the latter point also empirically, both on real and synthetic datasets. We show that variants of the recently suggested voting rule Rule-X (which satisfies proportionality) do very well in practice both with respect to social welfare and representation.