The objection
CLAIM-050 states the comparison over one state variable: “If P(V₂|Z) = G P(V₁|Z) for a source-independent garbling G, then V₁ is at least as good as V₂ for every bounded decision problem over Z”. Blackwell’s experiments share their parameter. THEORY-156: “An experiment is an n-tuple of probability measures on a common space, one per state”, and α is sufficient for β “if there is a stochastic transformation T with T m_i = M_i for every state i”. The outcome spaces of the two experiments may differ. The states i must be the same on both sides.
Two features of the translations the line cares about break the comparison as CLAIM-050 states it.
The situation changes. CLAIM-091 writes translation as (u, s, a, k, g) → (u′, s, a, k′, g′), achieving pragmatic equivalence “by compensating for changes in the social coordinates of an utterance through changes in its linguistic coordinates”. The source reader decides about a situation with coordinates (k, g). The target reader decides about one with (k′, g′). To compare their experiments one must say which target situation corresponds to which source situation, and index both by one parameter. That correspondence is one more that nothing fixes (QUESTION-005). The readers differ as well: CLAIM-074 makes fidelity relative to the interpreter’s learning history.
Where the situation is common, the rendering is not a garbling. A garbling needs the rendering to depend on Z only through the source text, V ⫫ Z | U. A translator who knows the context breaks that. So does compensation, which uses what the translator knows about the target audience. So does the deliberately adaptive translation of CLAIM-034, “one-way simulation where target audiences can reproduce the source utterance’s relevant communicative possibilities”. Outside garblings, Blackwell’s order is still defined. But it typically leaves source and target incomparable, and the direction the manuscript uses (CLAIM-050: “garbling implies no worse”) says nothing about them.
A worked case. Let Z be uniform on three situations, 1, 2 and 3.
- The source text tells its reader only whether Z = 1: U = 1 if Z = 1, and U = 0 otherwise.
- A translator who knows the setting tells the target reader only whether Z = 3: V = 1 if Z = 3, and V = 0 otherwise.
V is not a garbling of U, because given U = 0 it still varies with Z. And neither experiment is at least as informative as the other. Take the problem “say whether Z = 3”, with loss 1 for a wrong answer. From V the risk is 0. From U it is 1/3: on U = 1 the answer is certainly no, and on U = 0, which has probability 2/3, the two remaining situations are equally likely, so any answer is wrong half the time. For “say whether Z = 1” the risks are reversed. If either experiment dominated the other, it would do at least as well in every problem under every prior. So U and V are incomparable in Blackwell’s order. How far apart they are is a question for Le Cam’s deficiency, which THEORY-156 names and the record has not read (Torgersen, LIT-778).
So CLAIM-050’s precision covers garbling transports about an unchanged situation: a lossy retelling of one story, read by the same kind of reader. That is not the case the line cares about most. CLAIM-115 and CLAIM-139 both rest on CLAIM-050 for what makes a distinction decision-relevant.
What the record already holds nearby. QUESTION-016 holds the chain version open: “A garbling of a garbling is a garbling, so sufficiency for Q can only decline along a pure chain. The open part is the case the manuscript flags, interpreters with side information”. CLAIM-125’s first part asks for an informativeness order “taken across a change of cover”. Neither says that CLAIM-050’s comparison needs a common parameter, or that the line’s own central cases lack one.
What it does not say
- It does not say decision-relative fidelity is wrong. CLAIM-050’s first half stands. For a common situation, its prior art gives a bound that needs no garbling: with total variation, the posterior distortion bounds the extra Bayes risk of every bounded-loss decision (Zhao et al., as CLAIM-050 cites them, THEORY-161).
- It does not say Blackwell’s order is undefined outside garblings. It is defined for any two experiments on one parameter. What applies only to garblings is the direction the manuscript uses.
- It does not say compensation makes a translation worse. The worked case shows a rendering that is better for one decision and worse for another, which is what CLAIM-128 expects of fidelity profiles.
What would answer it
Either of two things.
- A comparison of experiments across a change of parameter, through a stated correspondence of situations z ↦ z′ with its own anchoring (QUESTION-005), and results for that comparison.
- A restriction of CLAIM-050 to decisions about a situation the translation does not change, with the side-information case (QUESTION-016) handled by a quantitative measure such as deficiency rather than by the order.
Where it stands
The record’s reply of 2026-10-10 is CLAIM-212. It answers this objection for report fidelity, where both readers decide about the source’s situation, so the parameter is common and Blackwell’s order gives a precise verdict, often incomparability: the worked case above is incomparable, as CLAIM-128 expects, and CLAIM-259’s directed decision term measures each direction of it. The objection stands for re-performance fidelity, which needs a correspondence of situations (QUESTION-005). Whether the line’s central cases are reports or re-performances is open, and CLAIM-212’s defeat condition says so. The objection stays Proposed.
Note of 2026-10-15: split under ADR-043
ADR-043’s full classification found this objection compound: its worked case is demonstrated, and its reading that the case is the normal translation case, through CLAIM-091’s compensation, is interpretive. The worked case is now CLAIM-323 (demonstrated), on which this objection rests. This claim keeps the rest: that Blackwell’s order, comparing experiments about one parameter, does not reach the line’s translations, and that the direction the manuscript uses is silent about them. Its title states that reading and is kept, and its warrant stays interpretive.
Note of 2026-10-27: grounded in what it uses of Blackwell
The status review of this date (ADR-057) moved this claim’s ground from THEORY-156 to THEORY-1096. It uses Blackwell’s definitions (an experiment, a garbling, the informativeness order) or the easy direction, that a garbling never helps a decision-maker free to choose any rule. Both hold on any outcome spaces, with the proof written out there. THEORY-156’s general converse, which stays Proposed, is not used. Quotations of THEORY-156 above are of the definitions it states.