Identifying Causal Backbones from Private Agent Reports

The concept of Relative Causal Knowledge (RCK) suggests that different agents, each with their own structural causal models, can exchange causal insights through a shared, interventionally consistent abstraction known as a "backbone." This research investigates a foundational question: when can this shared backbone be uniquely identified from the agents' private causal knowledge? Focusing on a basic scenario where two agents' private causes influence a single shared outcome, and each agent only identifies the causal marginal relevant to its own perspective, the study reveals a critical limitation. Under standard assumptions, these local causal marginals are insufficient to identify a unique backbone; an infinite number of joint intervention kernels could produce the same private reports while differing on joint interventions. However, the paper offers a conditional recovery result: if additive separability is present, the hidden interaction degree of freedom is removed. More importantly, identification becomes possible when agents communicate causally identified response functions, rather than just observational summaries. This highlights that the challenge is primarily a communication problem before it becomes a policy-composition problem.