We address the question of aggregating the preferences of voters in the context of participatory budgeting. We scrutinize the voting method currently used in practice, underline its drawbacks, and introduce a novel scheme tailored to this setting, which we call "Knapsack Voting". We study its strategic properties - we show that it is strategy-proof under a natural model of utility (a dis-utility given by the $\ell_1$ distance between the outcome and the true preference of the voter), and "partially" strategy-proof under general additive utilities. We extend Knapsack Voting to more general settings with revenues, deficits or surpluses, and prove a similar strategy-proofness result. To further demonstrate the applicability of our scheme, we discuss its implementation on the digital voting platform that we have deployed in partnership with the local government bodies in many cities across the nation. From voting data thus collected, we present empirical evidence that Knapsack Voting works well in practice.

中文翻译：

---

参与式预算的背包投票

我们解决了在参与式预算的背景下汇总选民偏好的问题。我们仔细研究了目前在实践中使用的投票方法，强调了它的缺点，并介绍了一种适合这种情况的新颖方案，我们称之为“背包投票”。我们研究了它的战略特性——我们表明它在效用的自然模型（结果与选民的真实偏好之间的 $\ell_1$ 距离给出的不效用）和“部分”策略下是策略证明的- 在一般添加剂实用程序下的证明。我们将背包投票扩展到更一般的有收入、赤字或盈余的环境，并证明了类似的策略证明结果。为了进一步证明我们方案的适用性，我们在与全国许多城市的地方政府机构合作部署的数字投票平台上讨论了它的实施。从如此收集的投票数据中，我们提供了经验证据，证明背包投票在实践中运作良好。