Jurimetrics

 ( Metrics ) 

In more male-dominated industries, such as Silicon Valley, there could be an even greater imbalance. Suppose that instead of parity in general, the probability that a person who is qualified for board service is female is 40%; this is likely to be a high estimate, given the predominance of males in the technology industry. Then the probability of violating Senate Bill 826 by chance may be recomputed as:

Suppose that there is some binary screening procedure for an action $V$ that identifies a person as testing positive $+$ or negative $-$ for the action. Bayes' theorem tells us that the conditional probability of taking action $V$, given a positive test result, is:$$\backslash mathbb\{P\}(V\; |\; +)\; =\; \{\backslash mathbb\{P\}(+|V)\backslash mathbb\{P\}(V)\backslash over\{\backslash mathbb\{P\}(+|V)\backslash mathbb\{P\}(V)\; +\; \backslash mathbb\{P\}(+|\backslash sim\; V)\backslash left1-\backslash mathbb\{P\}(V)\backslash right\}\}$$For any screening test, we must be cognizant of its sensitivity and specificity. The screening test has sensitivity $\backslash mathbb\{P\}(+|V)$ and specificity $\backslash mathbb\{P\}(-|\backslash sim\; V)\; =\; 1\; -\; \backslash mathbb\{P\}(+|\backslash sim\; V)$. The sensitivity and specificity can be analyzed using concepts from the standard theory of statistical hypothesis testing:

• Sensitivity is equal to the statistical power $1-\backslash beta$, where $\backslash beta$ is the type II error rate
• Specificity is equal to $1-\backslash alpha$, where $\backslash alpha$ is the type I error rate

Therefore, the form of Bayes' theorem that is pertinent to us is:$$\backslash mathbb\{P\}(V\; |\; +)\; =\; \{(1-\backslash beta)\backslash mathbb\{P\}(V)\backslash over\{(1-\backslash beta)\backslash mathbb\{P\}(V)\; +\; \backslash alpha\; \backslash left1-\backslash mathbb\{P\}(V)\backslash right\}\}$$Suppose that we have developed a test with sensitivity and specificity of 99%, which is likely to be higher than most real-world tests. We can examine several scenarios to see how well this hypothetical test works:

• We screen welfare recipients for cocaine use. The base rate in the population is approximately 1.5%, assuming no differences in use between welfare recipients and the general population.
• We screen men for the possibility of committing mass shootings or terrorist attacks. The base rate is assumed to be 0.01%.

With these base rates and the hypothetical values of sensitivity and specificity, we may calculate the posterior probability that a positive result indicates the individual will actually engage in each of the actions:

One example of an application of jurimetrics is through resource allocation within court systems, where data analytics are used to identify potential difficulties and suggests improvements. Another example is the analysis of disparities within sentencing. This allows policymakers to address the inequities within legal practices. These emphasize the role of jurimetrics in the legal system, as a way to bridge quantitative analysis, and equitable judicial processes.

• Bayesian inference
• Causal inference
• Instrumental variables
• Design of experiments
• Vital for epidemiological studies
• Generalized linear models
• Ordinary least squares, logistic regression, Poisson regression
• Meta-analysis
• Probability distributions
• Binomial distribution, hypergeometric distribution, normal distribution
• Survival analysis
• Kaplan-Meier estimator, proportional hazards model, Weibull distribution

Technological advancements such as AI have been used in creating legal analytics platforms. They can review large amounts of case law, and identify patterns that assist in crafting legal arguments. These innovations improve decision-making processes by reducing the likelihood of human error, but also increase the efficiency of legal research.

For example, recent studies highlight the efficiency of ML in analyzing complex datasets, such as those found in healthcare or legal domains, with high accuracy. One application discussed by Christian Garbin, Nicholas Marques, and Oge Marques (2023) involves the use of ML models to identify specific patterns in datasets characterized by class imbalances. The article discusses datasets related to opioid use disorder (OUD), and how judgements passed in legal environments have been dependent on these datasets that are connected closely to class imbalances.

Despite many advancements, the integration of AI into jurimetrics presents challenges. Garbin, Marques, and Marques emphasize that many studies that use machine learning algorithms fail to transparently document essential steps, such as data preprocessing, hyperparameter tuning, or the criteria used for splitting training and test sets.

Garbin, Marques, and Marques recommend prioritizing interpretable models unless the performance gap justifies the use of less transparent algorithms. Since legal decisions have high-stakes, interpretable models(logistic regression or decision trees) are often preferred over more complex "black-box" models. Often, these "black-box" models have higher predictive accuracy, but the interpretability is a central and ethical concern.