Partition aggregation for participatory budgeting

Recently, Jain et al. [IJCAI, 2019] studied the effect of project interactions in participatory budgeting (PB) by assuming an existing partition of the projects to interaction structures, namely a grouping of the projects into substitution and complementarity groups. Motivated by their study, here we take voter preferences to find such interaction structures. In our model, voters submit interaction structures, and the goal is to find an aggregated structure. Formally, given a set P of m projects, and n partitions of P, the task is to aggregate these n partitions into one aggregated partition. We consider this partition aggregation task both for substitution structures and for complementarity structures, studying several aggregation methods for each, including utility-based methods and Condorcet-based methods; we evaluate these methods by analyzing their computational complexity and their behavior with respect to certain relevant axiomatic properties.