Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome

Abstract

The Relativity of Causal Knowledge (RCK) explains how a network of agents with different structural causal models can exchange causal knowledge through a shared interventionally consistent abstraction, or backbone. We ask the prior identification question that this transport mechanism presupposes: when is that backbone determined by the agents'private causal knowledge? In the basic two-agent common-effect case, two private causes influence one shared outcome and each agent identifies only the single-cause causal marginal relevant to its own perspective. We show that, under standard compatibility, non-degeneracy, and local overlap assumptions, those local causal marginals do not identify a unique backbone. Infinitely many joint intervention kernels can induce exactly the same private reports while disagreeing on joint interventions. We then give a conditional recovery result. Additive separability removes the hidden interaction degree of freedom, but observational residual summaries remain insufficient. Identification becomes possible when agents communicate causally identified response functions. An education value-added example illustrates why this is first a communication problem, and only then a policy-composition problem.