Participatory budgeting is a democratic process for allocating funds to projects based on the votes of members of the community. However, most input methods of voters' preferences prevent the voters from expressing complex relationships among projects, leading to outcomes that do not reflect their preferences well enough. In this paper, we propose an input method that begins to address this challenge, by allowing participants to express substitutes over projects. Then, we extend a known aggregation mechanism from the literature (Rule X) to handle substitute projects. We prove that our extended rule preserves proportionality under natural conditions, and show empirically that it obtains substantially more welfare than the original mechanism on instances with substitutes.

中文翻译：

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替代项目的比例参与式预算

参与式预算是根据社区成员的投票为项目分配资金的民主过程。然而，大多数选民偏好的输入方式阻碍了选民表达项目之间复杂的关系，导致结果不能很好地反映他们的偏好。在本文中，我们提出了一种开始解决这一挑战的输入法，允许参与者表达项目的替代品。然后，我们扩展了文献中已知的聚合机制（规则 X）来处理替代项目。我们证明了我们的扩展规则在自然条件下保持了比例性，并根据经验表明，它在具有替代品的实例上获得了比原始机制更多的福利。