Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.

翻译：从观测到的相关性推断因果模型是一项极具挑战性的任务，对许多科学领域至关重要。为了减轻在给定观测数据中筛选可能因果解释时的计算负担，了解观测中的对称性是否对应于潜在实现中的对称性，从而能够快速排除不可能的因果解释，这一点非常重要。通过一个显式示例，我们证明，通常情况下，对称性无法被利用来缩减假设空间。我们使用一个基于三种独立经典随机性源实现的、关于二元事件的三角概率分布。我们证明，即使去除这些源分布物理系统受经典物理学描述的条件，以下三个要求也是不相容的：(i) 这些源分布相同的物理系统，(ii) 这些物理系统尊重相对论因果律，(iii) 相关性即为观测到的相关性。