Mathematical Techniques in Optimization and Statistics For Legal Decision-Making: A Framework for Evidence Evaluation, Discrimination Analysis and Risk Assessment
Author(s): Dr. R.N Agarwal
Publication #: 2609025
Date of Publication: 12.10.2026
Country: India
Pages: 1-7
Published In: Volume 12 Issue 5 October-2026
Abstract
Statistics has become an increasingly important component of legal research, litigation, judicial reasoning, and evaluation of scientific evidence. Legal decisions frequently involve quantitative questions concerning probability, discrimination, damages, risk, sampling, causation, and the reliability of expert testimony. However, statistical evidence can also be misinterpreted through inappropriate averages, sampling bias, the prosecutor’s fallacy, Simpson’s paradox, and confusion between correlation and causation.
This paper develops a mathematical and statistical framework for the application of statistical techniques to legal decision-making, with particular emphasis on the integration of statistical analysis and optimization. The framework considers chi-square testing for categorical evidence, probability and risk measures for causation analysis, sampling and extrapolation for class actions, regression-based analysis for discrimination claims, and confidence intervals and error rates for evaluation of expert evidence. An optimization perspective is introduced in which legal decision-making is formulated as a constrained statistical decision problem balancing evidential strength, uncertainty, error, and reliability.
Illustrative examples demonstrate how statistical techniques can quantify disparities and risks while mathematical optimization can assist in selecting decision rules under competing constraints. The paper also discusses the importance of statistical reliability in scientific-evidence assessment and highlights the need for transparent interpretation of statistical results in courts. The proposed framework provides a bridge between mathematical statistics, optimization techniques, and legal reasoning and may contribute to more objective, reproducible, and evidence-based judicial decision-making.
Keywords: Keywords: Legal Statistics; Mathematical Statistics; Optimization; Statistical Decision Theory; Chi-Square Test; Regression; Probability; Risk Assessment; Statistical Evidence; Discrimination Analysis; Expert Testimony.
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