The requirements for this method fixed what it takes, what it weighs, and what it must at least return, and left three things open: what an act's demand consists of, how the four comparisons combine into one verdict, and whether a verdict must carry a reason as well as a decision. This section settles all three. Each is argued from what the method demonstrably needs, and where a neighbouring field has already answered the question it is adopted rather than reinvented.
The account stops at the same place the record's did. It says what the method computes and on what grounds, and it does not give the signatures or types by which a library would express it. That belongs to the instantiation, and to a method that has first been argued.
What an act's demand consists of
The record deliberately does not hold the act's demand, because admissibility is a relation and a relation is not stored in either of the things it relates. That exclusion left the question of what a demand is, and only its shape was fixed: the act's side of the same axes the basis speaks on. Fixing its content is the first task here.
A demand is a set of four requirements, one for each comparison the method makes, stated by whoever proposes the act rather than by the claim or its producer. The required scope is the bounds within which the act needs the claim to hold: a valve, a unit, a plant. The staleness tolerance is the age beyond which the act will not accept a basis, expressed against the rate at which the underlying condition changes rather than as a bare interval, because an hour is fresh for a tank and stale for a trip. The accepted production is the set of acquisition and transformation kinds the act will act on, drawn from the same closed vocabularies the record uses, so that an act may accept a measurement and refuse a generation without either being described in prose. The accepted authority is the set of sources whose vouching the act will take, and whether a lapsed vouching still counts.
Two properties of this are worth stating because they are what make the demand a demand rather than a second basis. It is authored by the act and not by the claim, so a producer cannot lower the bar for its own output. And it is stated in the same terms as the record on every axis, so that each comparison is a comparison of like with like rather than an interpretation. Where a demand is silent on an axis, the axis does not constrain: silence is permission, not a default requirement, because a demand that quietly required what it did not state would refuse claims for reasons its author never gave.
How the four comparisons combine
This is the question decision theory was deferred to, and the reading changed what could be assumed. The worry was that decision theory would import a single number, since expected-utility theory ranks options by one, and a verdict that reduced to a scalar would be the confidence signal the review ruled out in a different notation. The scalar turns out to be a consequence of an axiom rather than of the theory. Completeness, the requirement that any two options be comparable, is what makes a single ranking possible, and many hold that it is not rationally required (Steele and Stefansson, 2020). Where it is dropped, preferences are represented by a set of probability-utility pairs and choice is made by a function returning an admissible subset under a constraint such as expected-utility non-dominance.
The method adopts the shape of that answer and not its machinery. The four comparisons are held simultaneously, no scale is imposed across them, and the combination is a rule over their outcomes rather than an arithmetic on their magnitudes. Concretely, the method is conjunctive: a basis is admissible for an act when it satisfies the demand on every axis, and inadmissible otherwise. Failure on any one axis is decisive, and the axes do not trade off.
Conjunction is a strong choice and the argument for it is that the alternatives are worse for this problem rather than that it is elegant. A trade-off rule would have to say how much freshness compensates for a weaker acquisition, and there is no exchange rate between them that is not invented: an act that requires a measurement is not made safe by a very recent generation. A scoring rule would reintroduce the scalar and with it the category error the review spent a chapter establishing, that a number about an estimation process is not a judgement about a particular claim and act (Gawlikowski et al., 2021). A rule that admitted on a majority of axes would let a claim through on the strength of the axes that happened to be easy. Conjunction is what the four axes mean if they are requirements at all, and an axis that could be traded away was not a requirement.
The cost is over-refusal, and the methodology declared over-refusal a failure rather than a safe harbour, so it is not waved through here. It is bounded by where the strictness actually sits. Conjunction is strict about the relation between a demand and a basis; it says nothing about how demanding a demand must be. An act with a permissive demand is admitted easily by the same conjunctive rule that refuses an act with a stringent one, and the discipline supplies no pressure toward stringency. Whether that bound holds in practice is exactly what the coverage and risk measurement is for, and the conjunctive rule is the thing being measured rather than something the measurement is arranged to protect.
What the verdict carries
The argument runs on both sides. Contestability is owed at this handover by the frameworks the review surveyed, since a high-risk system must be transparent enough for a deployer to interpret its output and use it appropriately (European Union, 2024), and those affected must be able to understand and challenge a decision (OECD, 2019). Against that stands minimality, and the finding that explanation is where such mandates are commonly approximated rather than met, the dominant post-hoc methods producing surrogates that give false assurances and do not evidence the acceptability of what they explain (Mittelstadt et al., 2018).
The conjunctive rule settles this more cheaply than either side of that argument expected. Because a refusal is a failure on a specific axis, the axis that failed is already known to the method at the moment it refuses; reporting it costs nothing and invents nothing. So a verdict carries the decision and, when the decision is refusal, the axis or axes on which the demand was not met, together with the demand and the basis value that were compared. It does not carry an explanation in the sense the explainability literature means, and this is the distinction that keeps the concession honest: the method reports which requirement was not satisfied, which is a fact about the comparison it performed, rather than an account of why a claim came to have the basis it has, which would be a surrogate for a history the method never had.
That boundary is what stops contestability from smuggling in the failure the review documented. A reason that reported the comparison is checkable against the record and the demand by anyone holding both. A reason that narrated the claim's history would be exactly the plausible account of behaviour the explanation critique establishes is not evidence of acceptability.
What the method does not do
Three limits are stated here rather than left for a reader to find. The method does not assess the truth of the claim, which was out of scope from the problem statement onward; a well-founded claim may be false and the method will admit it, because it judges the basis and not the world. It does not rank or compare claims, since admissibility is a relation between one basis and one act and there is no ordering across claims to be had from a conjunctive rule. And it does not decide what a demand should be. The demand is authored by whoever proposes the act, and the method's contribution is that the demand must be stated on the same axes as the basis and is then applied mechanically, not that the discipline knows what an act ought to require.
That last limit is the one a critical reader should press, because it locates precisely how much of the judgement has been mechanised. The discipline does not remove the need for someone to decide what an act requires of its evidence. It removes the need for that decision to be remade, informally and invisibly, at every handover, by requiring it to be stated once in terms a machine can compare against a basis that travelled with the claim. The judgement that remains human is the setting of demands, and it is made in advance, in the open, and is auditable. The judgement that has been mechanised is whether a particular basis meets a particular demand at the point of action, which is the judgement the review found every surveyed field handing to a person who, at a machine handover, is not there.
References
Steele, K. and Stefansson, H. O. (2020). Decision Theory. Stanford Encyclopedia of Philosophy. plato.stanford.edu/entries/decision-theory
Gawlikowski, J., Njieutcheu Tassi, C. R., Ali, M., Lee, J., Humt, M., Feng, J., Kruspe, A., Triebel, R., Jung, P., Roscher, R., Shahzad, M., Yang, W., Bamler, R. and Zhu, X. X. (2021). A Survey of Uncertainty in Deep Neural Networks. Artificial Intelligence Review. arXiv:2107.03342. arxiv.org/abs/2107.03342
European Union (2024). Regulation (EU) 2024/1689 (Artificial Intelligence Act), Article 13. Official Journal of the European Union. eur-lex.europa.eu
OECD (2019). Recommendation of the Council on Artificial Intelligence, Principle 1.3. OECD/LEGAL/0449. legalinstruments.oecd.org
Mittelstadt, B., Russell, C. and Wachter, S. (2018). Explaining Explanations in AI. FAT* 2019. arXiv:1811.01439. arxiv.org/abs/1811.01439