Goodhart as a non-faithful functor

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

Goodhart as a non-faithful functor is the manuscript’s formal sketch of a proxy mapping that forgets distinctions relevant in the world it measures. Optimization in the metric category can therefore fail to preserve the good sought in the original setting. The idea describes consequential loss under representation, not a completed categorical theorem or a claim that every use of measurement necessarily corrupts its object.

Explanation

PB presents a mapping from a world-oriented category into a metric category and describes it as non-faithful. The practical point is that distinctions lost in that mapping need not be recovered by maximizing its output. Its formal status remains a sketch, not a fully specified functor for every institution or an independently verified proof of Goodhart’s law.

RB3 gives the institutional content: throughput can displace continuity of care, publishable output epistemic integrity, and engagement shared sense-making. These are the manuscript’s pressure-test examples. They locate the ethical problem in the regime giving a proxy force, not only in an inaccurate number or a malicious individual.

The Coda adds path dependence: once institutions reorganize around a metric, correcting the number may not restore the world it has shaped. Measurement itself is not rejected; world-coupled answerability and practical correction remain necessary. The cited quantification tradition supplies provenance without turning the categorical analogy into a settled universal mechanism.

Scope and attribution

Preserve the analogy’s limited formal status and the regime-level consequence.

PB — The Possible Book

The non-faithful-functor presentation is an explicitly formal sketch.

Occurrence locators: 155, 156.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.