Proportional Participatory Budgeting with Projects Interaction

Abstract: Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of community members. PB outcomes are commonly evaluated for how they reflect voters preferences (e.g., social welfare) and the extent to which they are fair (e.g., proportionality). Due to practical and computational reasons, voters are usually asked to report their preferences over projects separately, possibly neglecting important dependencies among projects, which causes the outcome to no longer be proportional and achieve lower satisfaction. This work is the first to suggest a polynomial-time aggregation method capable of guaranteeing proportional outcomes under substitution dependencies. The method is a variant of the Method of Equal Shares, and we further provide another variation that can guarantee a more relaxed notion of proportionality for any type of dependency, and is FPT rather than polynomial. Through simulations, we demonstrate that these aggregation methods achieve, on average, higher social welfare than their counterparts that ignore the dependencies.