A Condorcet-Consistent Participatory Budgeting Algorithm
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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 and the produced budgets usually do not provide axiomatic guarantees. Here we apply the Condorcet principle to a general participatory budgeting scenario that includes a budget proposal, a vote profile, and a budget limit. We devise a polynomial-time budgeting algorithm that, given such a scenario, produces the Condorcet winner if it exists, else a member of the Smith set. (A caveat -- our definition of dominance employs strict rather than relative majority.) Furthermore, we argue that if there is no Condorcet winner for this scenario, then the resulting budget would often be close to a weak Condorcet winner for a slightly smaller budget limit. Our algorithm allows items to be quantitative, indivisible, and have arbitrary costs and allows voters to specify weak orders as their preferences. Furthermore, our algorithm supports hierarchical budget construction, thus may be applied to entire high-stakes budgets.
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