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Participatory budgeting (PB) has been widely adopted and has attractedsignificant research efforts; however, there is a lack of mechanisms for PBwhich elicit project interactions, such as substitution and complementarity,from voters. Also, the outcomes of PB in practice are subject to variousminimum/maximum funding constraints on 'types' of projects. We propose a novelpreference elicitation scheme for PB which allows voters to express how theirutilities from projects within 'groups' interact. We consider preferenceaggregation done under minimum and maximum funding constraints on 'types' ofprojects, where a project can have multiple type labels as long as thisclassification can be defined by a 1-laminar structure (henceforth called1-laminar funding constraints). Overall, we extend the Knapsack voting model ofGoel et al. [26] in two ways - enriching the preference elicitation scheme toinclude project interactions and generalizing the preference aggregation schemeto include 1-laminar funding constraints. We show that the strategyproofnessresults of Goel et al. [26] for Knapsack voting continue to hold under1-laminar funding constraints. Moreover, when the funding constraints cannot bedescribed by a 1-laminar structure, strategyproofness does not hold. Althoughproject interactions often break the strategyproofness, we study a special caseof vote profiles where truthful voting is a Nash equilibrium under substitutionproject interactions. We then study the computational complexity of preferenceaggregation. Social welfare maximization under project interactions is NP-hard.As a workaround for practical instances, we give a fixed parameter tractable(FPT) algorithm for social welfare maximization with respect to the maximumnumber of projects in a group when the overall budget is specified in a fixednumber of bits.

A Mechanism for Participatory Budgeting With Funding Constraints and Project Interactions