A Democratically-Optimal Budgeting Algorithm

The budget is the key means for effecting policy in democracies, yet its preparation is typically an opaque and arcane process. Participatory budgeting is making inroads in municipalities, but is usually limited to a small fraction of the total budget as its methods do not scale: They cannot handle quantitative budget items nor hierarchical budget construction. Here we apply the Condorcet principle to participatory budgeting. We say that a budget is globally-optimal if it is feasible (i.e., within the budget limit) and no other feasible budget is preferred over it by a majority of the voters. A globally-optimal budget does not always exist due to Condorcet cycles; hence, we settle for a democratically-optimal budget, which is globally-optimal up to such cycles. We devise a polynomial-time algorithm that, given a budget proposal, a set of votes (rankings) over it, and a budget limit, produces a democratically-optimal budget. We argue that in practice the resulting budget would most often be either globally-optimal or almost globally-optimal. Our method handles quantitative budget items of arbitrary cost and supports hierarchical budget construction, thus may be applied to entire budgets.