Budget Aggregation via Knapsack Voting: Welfare-maximization and Strategy-proofness

Participatory budgeting [1], which started in South America, is now gaining popularity in the US, with cities like San Francisco, Vallejo, Boston, Chicago and New York adopting this paradigm [6]. With decisions involving millions of dollars across the nation being made this way, a question arises as to how to design voting schemes to aggregate the voters’ preferences into a meaningful budget decision. And with many cities adopting digital voting, a key requirement is the amenability of these schemes to implementation via digital tools. There has been some work on addressing this question [4], where a class of schemes called Knapsack Voting (inspired by the classical Knapsack Problem [5]) was proposed. In particular, two elicitation schemes: one, where the budget constraint is imposed on each vote, and two, where voters compare different items on the ballot according to their value-for-money, (i.e., the perceived benefit to society per dollar spent on each item); and appropriate aggregation rules for each, were introduced. We will refer to the former scheme, along with its aggregation rule, as Knapsack Voting. In this paper, we show that under a natural model of voter utilities, the Knapsack Voting rule is both strategy-proof and welfare-maximizing. In addition, we provide an empirical comparison between Knapsack Voting and K-approval voting, which is the method currently used in most Participatory Budgeting elections. We see that Knapsack Voting leads to a more economical consideration of projects on the ballot. To do this, we use data collected from the digital voting platform (pbstanford.org) that we have deployed in partnership with the local government apparatus in many cities across the nation.