MMP.19:4.4 - Evaluate the compared responses with that common basis

Replace the selected mechanisms using C.28.MR. At each retained u, evaluate all the responses needed by the question before averaging. For a finite conditional comparison,

P(Y_a=y, Y_b=z given e)
    = sum_u w(u given e) 1[Y_a(u)=y and Y_b(u)=z].

Here the indicator is one when both conditions hold. A single response or expected difference uses the corresponding function inside the same sum. The shared u preserves the modeled relation between alternatives. Use integration when the model supports a continuous version of this operation.

For a nested response Y_(a,M_b)(u), first compute the intermediate value M_b(u) under b. In the second model set A to a and M to that computed value for the same u, then evaluate Y. Averaging M_b before this replacement generally changes the target. The construction defines a model consequence even when no available physical procedure can jointly realize every term; C.28:4.5 governs a separate claim about obtaining samples.

For a pathway decomposition, state both component contrasts and verify that their sum is the intended total. Interactions can make another choice of reference mechanism give different components. A component’s numerical size does not by itself establish the adequacy of the explanation or the feasibility of a proposed physical intervention.