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CASE-154: One representation, two tasks, one bounded observer: with X₁, X₂ independent fair bits and an observer that reads one coordinate and cannot compute XOR, the raw pair U = (X₁, X₂) gives error 50% on Q_A = X₁ ⊕ X₂ and 0% on Q_B = X₁, and the compressed V = X₁ ⊕ X₂ gives 0% and 50%; a legibility regime can enable one perspective's distinction while disabling another's, with no task-independent sense in which it is better

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Properties7
StatusActive
Standingstipulated
Kindconstruction
Tagsinformation-theory, self-governance, epistemology
Linedistributed-agency
IllustratesCLAIM-199 — Blackwell's order bounds what a rendering makes possible for any receiver, and a given receiver's access is usable information relative to the rules it can apply, which a garbling can raise for that receiver but never above what the source makes possible, CLAIM-448 — An ordinal potential describes only the winning-move relation it is computed on; where an organization's legibility regime selects which contests are admitted or recorded, an acyclic record, even a persistent potential, can be the product of selective contestation, so observed coherence is not evidence that the organization's perspectives are integrated, and an intervention that improves its self-governance may at first increase the disagreement observed
Cited as “grounds” byCLAIM-455 — For one bounded observer, a transformation of a representation can make one task's distinction legible and another's illegible at once, so legibility regimes are ordered only relative to a task, and a regime that improves one perspective's competence can disable another's

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The case

X₁, X₂ independent fair bits. A bounded observer can read one coordinate of what it is given and cannot compute XOR. Two tasks: Q_A = X₁ ⊕ X₂ and Q_B = X₁.

taskerror from raw U = (X₁, X₂)error from compressed V = X₁ ⊕ X₂
Q_A50%0%
Q_B0%50%

From U the observer reads X₁, which is independent of X₁ ⊕ X₂, so Q_A is at chance, and Q_B is exact. From V, Q_A is exact, and V is independent of X₁, so Q_B is at chance. An ideal observer solves both from U. The bounded one cannot. This is CLAIM-199’s point made two-sided: a transformation can create usable information for a restricted observer (TERM-064) and, for the same observer, destroy usable information for another task.

What it can show

That a learned legibility regime can be competence-enhancing for one perspective and disabling for another, with no task-independent sense in which it is better or worse. An institution’s reporting can get better at forecasting output and worse at registering a grievance; a defensive process can learn an excellent threat representation that is poor at finding safe engagement.

What it cannot show

That a regime that disables a perspective is a governance failure. Before calling it one, it has to be shown that the representational resources could have served both demands at once (CLAIM-357’s structural conflict against avoidable shortfall). A real resource limit is a different failure from an authority structure that excludes a feasible alternative.

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