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.

翻译：在许多因果推断问题中，多个行动变量（如中介变量、因子、网络单元或基因型）共享相同的因果角色，但缺乏自然排序。为避免解释上的歧义，因果估计量应在重新标记下保持不变，这一隐含原则我们称之为置换不变性。我们正式刻画了这一原理，分析了其用于验证的代数与组合结构，并提出一类加权估计量——它们在保持置换不变性的同时能够捕捉所有阶数的交互效应。我们进一步提供了权重选择指南，以获得无残差估计量（其容斥求和能捕捉最大效应），并将结果推广至比率效应度量。