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.

翻译：参与性预算编制是一个向基于社区成员投票的项目分配资金的民主过程,然而,选民偏好的大多数投入方法使选民无法表达项目之间的复杂关系,导致的结果不能充分反映他们的偏好;在本文件中,我们提出了一个投入方法,通过让参与者表达项目替代物来应对这一挑战;然后,我们将文献中已知的汇总机制(规则X)扩大到处理替代项目。 我们证明,我们扩大的规则在自然条件下保持了相称性,并用经验表明,它所获得的福利大大高于最初的替代物机制。