标题： 关于因果估计量的排列不变性原理 显示英文标题

标题： On the permutation invariance principle for causal estimands

摘要： 在许多因果推断问题中，多个行动变量具有相同的因果作用，如中介变量、因素、网络单元或基因型，但缺乏自然的顺序。 为了避免解释上的歧义，因果估计量在重新标记下应保持不变，我们将其称为排列不变性的隐含原则。 我们正式描述了这一原则，分析了其代数和组合结构以进行验证，并提出了一类排列不变的加权估计量，这些估计量能够捕捉所有阶次的交互作用。 我们进一步提供了选择权重的指导，以产生无残留的估计量，其包含-排除和捕捉最大效应，并将我们的结果扩展到比率效应度量。 显示英文摘要

摘要： In many causal inference problems, multiple action variables share the same causal role, such as mediators, factors, network units, or genotypes, yet lack a natural ordering. To avoid ambiguity in interpretation, causal estimands should remain unchanged under relabeling, an implicit principle we refer to as permutation invariance. We formally characterize this principle, analyze its algebraic and combinatorial structure for verification, and present a class of weighted estimands that are permutation-invariant while capturing interactions of all orders. We further provide guidance on selecting weights that yield residual-free estimands, whose inclusion-exclusion sums capture the maximal effect, and extend our results to ratio effect measures.