More Determinate and Less Settled

The question

Mitchell Berman's principled positivism holds that legal content is fixed by a weighted balance of legal principles, each contributing force in proportion to its weight and to how strongly the facts of a case activate it.

A principle's weight is how much it counts in the legal system generally. Its activation is how strongly it bears on the case at hand. The theory says the weights are grounded in legal practice, but it does not say what practice is, or how a pattern of practice fixes a number. This project gives the account its first systematic computational test, implementing it faithfully, varying its parameters across ranges no thought experiment could canvass, and measuring the results against what the theory itself requires.

Two findings

Principled positivism therefore does not resolve the indeterminacy it inherited from Hart and Dworkin. It relocates it, from how principles combine, which it handles well, to which practice grounds the weights, and to the prior question of how legal grounds themselves change.

The four requirements

Every mechanism and every aggregation rule is held to the same four requirements, each drawn from something Berman claims or commits to, and each scored seed by seed across thirty random seeds.

Weight gradation and correlation benefit are measured but are not requirements. Berman's account, unlike Dworkin's, permits principles to carry equal weight, so no pass-or-fail verdict may depend on them.

The four mechanisms

Reliance and appointment correlate at +0.93, closely enough that the two are in effect one structure. Uptake opposes both, at −0.78 and −0.75. So the four dynamics realize three distinct structures, not four.

Three Harts, kept distinct

The argument runs three separate Hartian comparisons, and they are never conflated.

• A Hartian validation rule is the contradiction foil. It asks of each standard only whether it is valid and which way it points, so on a genuine conflict it certifies both sides at once.
• The hierarchical Hart is the determinacy baseline. It sorts the principles into ranked tiers and decides at the highest tier holding an applicable principle, and only where enough of that tier's principles point the same way.
• A consensus Hart is a flat share bar, deciding when a fixed share of the principles agree.

Results

Every figure below is computed on synthetic cases with independent activations, the conservative baseline, so each should be read as a floor. Correlation only improves the model's performance. The one exception is the margin over Hart, which reverses under category-correlated activations and is reported as such.

The computational supplement

Ten notebooks, a shared engine, and the saved outputs behind every number above. All results were verified in Google Colab, run in dependency order, with each notebook carrying its own self-checks.

Every notebook above is downloadable from this page, as is the saved output behind each number. To run them:

Notebooks 0 and 7 should be run before 8, which reads their summary JSON. The engine is computational/berman_core.py; it is duplicated inside notebooks/ so a Colab session can import it without a path fixup, and the two copies are byte-identical.

Citation

@software{kamper_berman_supplement_2026,
  author    = {Kamper, David G.},
  title     = {Computational supplement to "More Determinate and
               Less Settled"},
  year      = {2026},
  version   = {1.0.0},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.24121884}
}

@article{kamper2026determinate,
  author = {Kamper, David G.},
  title  = {More Determinate and Less Settled},
  year   = {2026},
  note   = {Manuscript}
}