1. From Symmetric Comparison to the Chain — Why "Human vs. AI" Is the Wrong Unit of Analysis
The most recurring objection among the five adversarial reviews gathered for this article does not target any individual component of the LME — it targets the very architecture of the comparison. Formulated most precisely by one of them: if the human receives an environment and can modify it through the decision, and the LLM, in isolation, cannot, then placing and side by side — as though they were, on their own, parallel and sufficient assessments of the quality of two elements situated equivalently within the causal chain — presupposes a structural equivalence that most real systems simply do not have. In the human-in-the-loop systems this article considers, the AI recommends — or prioritizes, flags, proposes — and the human supervisor retains the final decision, accepting, modifying, or rejecting that output. The true object is not Human vs. AI — it is Human + AI + Environment, and treating it as a binary comparison is, literally, comparing entities that occupy different positions in the causal chain linking the environment to the consequence.
This objection has more reach than it might appear at first glance, because it does not only affect recent attempts to audit algorithmic decision-making — it also runs through much of the established literature on algorithm aversion and appreciation. That literature typically measures acceptance, trust, or the weight assigned to algorithmic advice — variables indispensable for understanding human reliance — without formalizing the two-stage structure, environmental cue → recommendation → decision, that the very notion of "advice" already implies. When Kaufmann and colleagues (2023) propose situating each algorithmic advice task along the CCT's intuition-analysis continuum, what is implicitly at stake is precisely this two-stage structure; but the proposal remains at the level of receptivity to advice, not at the level of formally auditing the chain linking the environment, the recommendation, and the final decision.
There is, however, a closer formal precedent, and it is worth starting there before proposing an extension: Beckstead's (2017) Bifocal Lens Model Equation. Beckstead confronts a structurally analogous problem within clinical judgment — the distance between the risk assessment a physician produces and the intervention decision that same physician subsequently makes. His solution is to decompose clinical judgment into two linked layers, each with its own LME, allowing one to ask separately "does the physician assess risk well?" and "does the physician correctly convert that risk into the clinical decision?" — two questions the classic, single-layer LME collapses into one.
The Bifocal LME is the right precedent, but it solves a different problem from the one proposed here. In Beckstead, the two layers belong to the same agent — it is the same physician who assesses the risk and who then decides on the intervention; the "bifocality" lies in the task, not in the number of agents involved. The problem the five reviews raise is different: it is not a single agent performing two successive judgments, it is two distinct response policies — an observable algorithmic policy and a human supervisor's decision policy — in which the output of the first itself becomes an input cue for the second, and only the second's decision closes back onto the real environment. The extension proposed in this article inherits Beckstead's two-layer logic but changes what each layer represents: not two tasks performed by the same agent, but two distinct response policies, chained in series, in which the output of the first functions as an input cue for the second — and, critically, with the relationship between the final decision and the environmental criterion placed explicitly at the closing of the chain. Beckstead's BiLME was designed to decompose the cohesion between clinical judgment and treatment decision, not to model the propagation of a recommendation produced by another agent, nor the subsequent effects of the decision on the environment — it is this difference in formal objective, more than any temporal limitation of the original design, that justifies the extension.
This reformulation was already latent in the previous article of this series, even if not formalized: there, the human supervisor was described as "judge of the judge" — a review system that receives, through dashboards and alerts, cues about the performance of a cyber-physical loop it does not directly observe itself. What was missing — and is this article's architectural contribution — was to give that intuition an analytical form that would allow separating the chain's stages and formulating diagnostic hypotheses about where cue-criterion correspondence degrades: in the algorithmic policy, in the human integration of the recommendation, or in the definition of the criterion itself. It is not claimed, therefore, that the chain already has a single algebraic decomposition analogous to the classic LME; it is claimed that it provides the unit of analysis necessary to make such an audit possible. It is this architecture that the following section formalizes.