Computational Jurisprudence:
Testing Berman's Principled Positivism Through Agent-Based Modeling

David G. Kamper
University of California, Los Angeles
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Abstract

Mitchell Berman's principled positivism proposes that legal principles aggregate through Simple Additive Weighting, with each principle contributing force proportional to its weight and activation. This Article subjects the theory to the first systematic computational analysis. The SAW model tolerates substantial weight uncertainty, handles conflicting principles, and delivers significantly more determinacy than Hart's consensus-based alternative. An agent-based model shows that principle weights can emerge from simulated legal practice, but the emergent weights are binary (fully entrenched or dead), lacking the graded variation the model requires. Different practice mechanisms, moreover, produce incompatible weight structures: evolutionary selection achieves differentiation without gradation, while strategic optimization achieves gradation without differentiation. This mechanism dependence is the Article's central contribution: Berman's claim that parameters are "practice-grounded" requires specifying which kind of practice generates them.

Notebooks

All notebooks run in Google Colab. Click to open directly in your browser.

Notebook 0: Static Properties

Tests Berman's SAW model with stipulated parameters across 9 experiments.

~20 min CPU 20 seeds
Open in Colab

Notebook 1: ABM Emergence

Simulates 100 judges across 4 methodologies. Tests whether weights emerge from practice.

~45 min CPU (High-RAM) 20 seeds
Open in Colab

Notebook 2: Mechanism Dependence

Compares ABM, MARL, and Hybrid mechanisms. The central finding.

~90 min T4 GPU 10 seeds
Open in Colab

Publication Figures

Generates all 11 figures (8 main + 3 supplementary) from exported data.

~5 min CPU 600 DPI
Open in Colab

Key Results

Finding Value Source
Mean weight tolerance (σ*)±0.165Notebook 0
Berman vs. hierarchical Hart+19.1%Notebook 0
Berman vs. consensus Hart (50%)+33.1%Notebook 0
Balanced-conflict determinacy76.8%Notebook 0
Cardinal vs. ordinal advantage3.3×Notebook 0
Dip test (Berman fitness)20/20 rejectNotebook 1
SAW fidelityr = 0.9994Notebook 1
ABM weight CV0.895Notebook 2
MARL weight CV0.344Notebook 2
C2 pass rate (all mechanisms)0%Notebook 2

Figures

Figure 1
Figure 1. Weight uncertainty tolerance. Threshold choice dominates all other parameters.
Figure 2
Figure 2. Berman's determinacy advantage over six Hart variants.
Figure 3
Figure 3. Bimodal weight differentiation under Berman fitness.
Figure 5
Figure 5. Complementary failure: ABM and MARL fail on different criteria.
Figure 6
Figure 6. Hart curve with emergent weights. Advantage narrows only against hierarchical Hart.
Figure 8
Figure 8. The complete three-stage argument.

All 11 figures available as PDF and PNG in the figures/ directory.

Data

All experimental results are exported as CSV files, organized by notebook. The Publication Figures notebook reads these CSVs to generate every figure in the paper.

Notebook 0 data (20 CSVs) Notebook 1 data (7 CSVs) Notebook 2 data (9 CSVs)

Citation

@article{kamper2026computational,
  author  = {Kamper, David G.},
  title   = {Computational Jurisprudence: Testing Berman's
             Principled Positivism Through Agent-Based Modeling},
  year    = {2026},
  note    = {Manuscript}
}