Participatory budgeting (PB) has been widely adopted and has attracted
significant research efforts; however, there is a lack of mechanisms for PB
which elicit project interactions, such as substitution and complementarity,
from voters. Also, the outcomes of PB in practice are subject to various
minimum/maximum funding constraints on 'types' of projects. There is an
insufficient understanding of how these funding constraints affect PB's
strategic and computational complexities.
We propose a novel preference elicitation scheme for PB which allows voters
to express how their utilities from projects within 'groups' interact. We
consider preference aggregation done under minimum and maximum funding
constraints on 'types' of projects, where a project can have multiple type
labels as long as this classification can be defined by a 1-laminar structure
(henceforth called 1-laminar funding constraints). Overall, we extend the
Knapsack voting model of Goel et al. in two ways - enriching the preference
elicitation scheme to include project interactions and generalizing the
preference aggregation scheme to include 1-laminar funding constraints.
We show that the strategyproofness results of Goel et al. for Knapsack voting
continue to hold under 1-laminar funding constraints. Although project
interactions often break the strategyproofness, we study a special case of vote
profiles where truthful voting is a Nash equilibrium under substitution project
interactions. We then turn to the study of the computational complexity of
preference aggregation. 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
maximum number of projects in a group