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arXiv 2104.05082cs.MA
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具有统一成本(或最多四个项目)的审批前置审批的核心是非空的

The Core of Approval Participatory Budgeting with Uniform Costs (or with up to Four Projects) is Non-Empty

Reshef Meir

摘要:

在批准替代性审批问题中,如果代理在$W'$中严格批准更多的项目,则她更喜欢一组项目$W'$而不是$W$。如果不存在其他项目集$W'$和代理集$K$两者都偏好$W'$胜过$W$并且可以资助$W'$,则项目集$W$处于核心。即使项目成本是一致的,核心是否可以是空的,这是一个悬而未决的问题。后一种情况称为多赢家投票核心。我们表明,在任何情况下,统一的成本或最多四个项目(和任何数量的代理),核心是非空的。

英文摘要:

In the Approval Participatory Budgeting problem an agent prefers a set of projects $W'$ over $W$ if she approves strictly more projects in $W'$. A set of projects $W$ is in the core, if there is no other set of projects $W'$ and set of agents $K$ that both prefer $W'$ over $W$ and can fund $W'$. It is an open problem whether the core can be empty, even when project costs are uniform. the latter case is known as the multiwinner voting core. We show that in any instance with uniform costs or with at most four projects (and any number of agents), the core is nonempty.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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