Opening — Why this matters now
Legal AI has a habit of oversimplifying judgment. In the race to automate legal reasoning, we have learned how to encode rules, then factors, and eventually hierarchies of factors. But something stubborn keeps leaking through the abstractions: strength. Not whether a reason exists — but how strongly it exists.
The paper under discussion enters this debate with surgical precision. It responds to a sustained critique by Trevor Bench-Capon, who argues that hierarchical factor models of precedent quietly fail when intermediate legal concepts are supported with unequal force. The authors agree with the diagnosis — but not with the proposed cure.
Their conclusion is subtle and slightly uncomfortable for purists: if you want coherent precedent, you cannot avoid graded reasoning.
Background — From flat factors to hierarchical fragility
Early models of precedential constraint treated cases as bundles of binary factors: present or absent, pro or con. This worked — until it didn’t. Once intermediate concepts (“behaved at home”, “acted reasonably”, “commercially sensitive”) entered the picture, flat models lost traction.
Hierarchical Result Models (HRM) attempted to fix this by stacking factors into abstraction layers. Base facts support intermediate factors; intermediate factors support outcomes. Elegant. Formal. And, as Bench-Capon showed, sometimes wrong.
The core criticism is devastatingly simple:
Two cases can satisfy the same intermediate factor — but not with the same strength.
Binary hierarchies cannot express this. Either an intermediate factor holds, or it does not. Reality, inconveniently, disagrees.
Analysis — Where the criticism lands (and where it doesn’t)
The authors do not deny the problem. Instead, they make two precise moves.
First, they show that factor-based HRMs are more flexible than critics assume. Whether intermediate factors constrain future cases depends on whether those factors are explicitly represented in the case description. This modeling choice matters — and courts (or parents, in the paper’s running ice-cream example) often leave it implicit.
Second — and more importantly — they argue that Bench-Capon’s strongest intuitions already assume dimensions, not factors.
If we say:
- Folding clothes establishes “tidiness” a little,
- Making the bed establishes it more,
- Interrupting a teacher undermines “good behavior” more than daydreaming,
then we are no longer reasoning in binary. We are reasoning along ordered scales.
At that point, insisting on factor-only representations becomes an act of denial.
Findings — Dimensions do the quiet work factors can’t
The paper introduces the Dimension-Based Hierarchical Result Model (DHRM) as the natural generalization. Instead of asking whether a factor applies, it asks:
To what degree does this dimension favor one outcome over another?
Each dimension carries an internal ordering. Hierarchies still exist, but now they propagate bounds, not Boolean truth.
| Model | Represents strength? | Handles unequal intermediate support? | Keeps hierarchy? |
|---|---|---|---|
| Flat Result Model | ❌ No | ❌ No | ❌ No |
| Hierarchical Factor RM | ❌ No | ⚠️ Partially (modeling-dependent) | ✅ Yes |
| Dimension-Based HRM | ✅ Yes | ✅ Yes | ✅ Yes |
In worked examples, the DHRM produces exactly the outcomes Bench-Capon expects — without abandoning intermediate concepts. The difference is not philosophical. It is structural.
Implications — What this means beyond legal theory
This paper is nominally about AI & Law. In practice, it is about any system that explains decisions using abstractions:
- Credit scoring models with layered risk indicators
- Medical decision systems with symptom → syndrome → diagnosis pipelines
- AI compliance tools mapping low-level signals to regulatory judgments
If intermediate concepts matter — and they usually do — then their internal gradation matters too.
Binary abstractions are cheap. Dimensions are honest.
For practitioners building AI systems that must justify outcomes (not just predict them), the message is clear: explanation models must carry quantitative structure all the way up the hierarchy, or they will quietly mislead.
Conclusion — Precision beats purity
Bench-Capon was right to point out the flaw. Where he hesitated was in following the implication to its logical end.
Hierarchies alone do not solve precedential reasoning. Hierarchies over dimensions do.
The contribution of this paper is not rhetorical. It is architectural. It shows that once we accept graded support — which courts, humans, and models already do — the right response is not to flatten the law back into factors, but to let abstractions carry weight.
Uncomfortable, perhaps. Necessary, certainly.
Cognaptus: Automate the Present, Incubate the Future.