Germinal G. Van

# The Application of Mathematics and Statistics to Legal Analysis

Perhaps many do not know or may not be familiar with this fact, but the study of the law does not escape the application of quantitative methods in its discipline. Indeed, mathematics and statistics are regularly applied to the law to solve some crucial legal issues such as jury discrimination, jury selection, or predict which rule of evidence will be used during trial. Mathematics and statistics are essentially used in criminal and civil law to determine potential jury outcomes.

The importance of mathematics in the administration of justice has risen with the growth of identification forensics and its influence continues to permeate questions of proof and judgment.[1] Probability theory is the main mathematical method used in the law to analyze legal problems because the fundamental characteristic of the law is based on uncertainty. In the book *Quantitative Methods in Law* (1978), Michael Finkelstein argued that legal thought is threaded with assessments of probability and descriptions of a statistical nature. In this book, the author uses statistical analyses to demonstrate that true legal issues often cannot be understood without the application of certain mathematical methods such as the multiple regression analysis.[2] In addition to jury discrimination and voting problems, statistical techniques are also applied to such issues as the meaning of ‘preponderance of evidence’, the probative force of statistical identification evidence, the measurement of economic concentration, solvency control for insurance companies…etc.[3]

In legal context, probability can help fact-finders assess the impact of evidence on the truth or otherwise of a particular proposition.[4] Evidence may, on occasion, point directly to incriminating or exculpating a suspect of a particular crime, but will more likely have a probative value in discriminating between competing propositions for either the source of some material found in relations to a scene of the crime or an alleged activity connected to a crime.[5] Evaluation of evidence using the likelihood ratio often involves the use of datasets and statistical assumptions.[6] The likelihood ratio is the probability of the evidence that proposition is true A divided by the probability of the evidence assuming that proposition B is true.[7] Hence likelihood ratios are generally attached to DNA evidence in which a ‘match’ of some degree is found between suspect’s DNA profile and the DNA profile derived from a trace found at the scene of the crime.[8]

Regression analysis is extensively used in litigation. And the goal of using regression analysis is to convert an observation of correlation into a statement of causation.[9] Regression analysis is crucial in litigation because it establishes a causal relationship between a defendant’s alleged misconduct and a plaintiff’s damages when direct evidence of harm is absent.[10] For example, regression analysis is used in cases of employment discrimination to show a causal relationship between certain alleged discriminatory conduct and hiring, firing, or promotion decisions.[11]

To conclude, mathematics and statistics have been playing a crucial role in solving some important legal issues. They have helped attorneys and litigators use the scientific method to strategize case outcomes and jury decisions.

[1] Strutin, Ken. “Calculating Justice: Mathematics and Criminal Law” *Law and Technology Resources for Legal Professionals. *(2013).
[2] Finkelstein, Michael O. *Quantitative Methods in Law: Studies in the Application of Mathematical Probability and Statistical to Legal Problems.* (1978).
[3] Ibid.
[4] Biedermann, Alex; Champod, Christopher; Hutton, Jane; Jackson, Graham; Lord Kitchin, Neoclous, Tereza; Spiegelhalter, David; Willis, Sheila; Wilson, Amy. “2. Probability and the Principles of Evaluating Scientific Evidence.” *The Use of Statistics in Legal Proceedings: A Primer for Courts. *(2020). The Royal Society of Edinburgh. p.13. ISBN: 9781-78252-486-1
[5] Ibid. p. 13
[6] Ibid. p. 16
[7] Ibid. p. 17
[8] Ibid. p. 17
[9] Litigation Services IMS Experts. “Regression Analysis in Litigation.” *The National Law Review. *(2014). Volume 11, Number 213.
[10] Ibid.
[11] Ibid.