A comparison can be correct and still answer too little

Consider a constructed inquiry about a pumping arrangement. One formulation concerns rated capacity; another concerns access to assistance when roads fail. The second changes the boundary and model question. A capacity model does not establish that people can reach help or that a mobile pump can be deployed. PSDA.1–3 preserve those differences before a comparison is used.

For an illustrative analytical slice, fixed pumps have losses 2 with normal roads and 3 with road access lost, at cost 8. Mobile pumps have corresponding losses 1 and 9, at cost 5. With assumed road-loss probability p and cost weight λ, lower-is-better scores are 2 + p + 8λ and 1 + 8p + 5λ. Fixed pumps score lower when 7p > 1 + 3λ. At λ = 0.5, the mobile score is lower for p = 0.2, but the fixed score is lower for p = 0.6.

PSDA.6 keeps the assumed trade-off distinct from protected service conditions. PSDA.7 keeps the missing probability basis visible. PSDA.8 supplies the conditional comparison and PSDA.9 exposes its reversal. Neither assumed input is established by this arithmetic. The incumbent and a staged direction may also remain live outside this two-option slice. A whole-investment recommendation therefore requires additional qualified premises or a narrower return.

Now suppose deployment is unavailable in the required window. The mobile branch loses its applicability; inserting a convenient probability cannot repair it. The fixed-option arithmetic remains valid at its stated scope. A professional adviser uses PSDA.14 to return what the recipient can rely on, while the governing decision remains separate. An analyst studying the relation for understanding can instead stop with the bounded model result.