Hello,
The recent in-press AMR paper "The Causal Inference Problem:.. " presents a formal model of organizations as causal systems to examine a causal inference problem faced by managers. This problem arises when leaders attempt to predict the consequences of their actions, especially when hidden factors are present. The authors argue that these hidden influences only create biased assessments of expected outcomes under a specific, problematic structure-when a hidden factor influences both an observed action and its immediate consequences (see Figures 2 and 4 of the paper). Importantly, the paper proposes formally (see Proposition 1) that managers can often accurately predict the effects of interventions even with simple or incomplete theories, provided this problematic structure is absent.
My concern is with the main proposition's claim that inferences are correct "..if and only if no hidden factor directly influences both that action and any factor directly influenced by that action", which is further specified as: the correct inference "..only fails under one local condition: when the action being intervened upon and one of its immediate consequences share a hidden common cause".
However, this can be disproved by inserting a near-identity matrix 'b' [0.99, 0.01; 0.01, 0.99] between 'a' and 'w' in Figure 4, where 'b' is not influenced by the hidden factor that influences 'a' and 'w'. Here, 'b' ensures 'w' is not directly influenced by 'a' (and that 'b' – as an immediate consequence of 'a' – does not share a hidden common cause). When 'b' is inserted – ensuring that the conditions are not met in Proposition 1 – the inferences remain incorrect, thus disproving the proposition. The intuition is that 'b' provides almost zero new information, so it is unlikely to act as a significant key to solving an informational problem (of inference).
The practical concern is that when 'b' is inserted, the reasonable reader identifies 'b' as the immediate consequence. Since 'b' is unconfounded by the hidden factor, the reader is misled into concluding the system is identifiable, when the underlying bias persists.
[Note that Proposition 1 is presented as applying an "important result from the structural causal modeling literature in computer science, in Tian and Pearl (2002)" to provide a complete characterization. However, Theorem 3 in that paper states that PX (V) is identifiable "if and only if there is no bidirected path connecting X to any of its children". However, the Tian paper's own Figure 3 example, which is asserted to be identifiable, explicitly includes a bidirected path between the intervention variable X1 and its child X3 (via unobserved factors U1 and U3 ). This discrepancy confirms that the necessary condition of the foundational theorem (the "only if" part) is contradicted by its own illustrative example.]
So, the challenge offered is to agree or disagree with this disproof (of Proposition 1), the latter expected with a reasonable (e.g., detailed) explanation please.
Thank you for any constructive feedback!
Richard