MMP.19:11 - SoTA-Echoing

Correa and Bareinboim (2025), Definitions 1.1–1.3 and §2.1.1, supply the shared-input and nested-response semantics used in :4.2–:4.4. The finite examples here use those definitions; the richer graphical calculus has further conditions and operations.

Mueller and Pearl (2023) separate average effects from probabilities of benefit or harm. Dawid and Senn (2025, v2), §§2–4, supply a serious alternative: intervention distributions suffice for maximizing expected realized outcomes under the stated information and constraints. Adopt the target distinction in :4.1/:4.6. In :5.2 the same two models require a joint account for the historical question but no such recovery for the stated future choice. The changed question justifies the more elaborate construction.

Raghavan and Bareinboim (2026, preprint), §§2 and 4–5, distinguish identification, partial identification and physically realizable counterfactual sampling. Adapt those distinctions in :4.4–:4.5. Their available-action, finite recursive and positivity assumptions limit the algorithmic results. Establishing a model consequence leaves its physical sampling conditions to be established separately when sampling is needed.

Reopen the selected construction when a supported additional mechanism or information source changes the compatible comparisons, or when another method obtains the required answer with less unsupported structure or burden. The worked finite constructions establish their stated mathematical consequences; practical validity still depends on the subject account.