# How Math Influences Legal Decisions

### Sunday November 05, 2023

###### •  statistics • forensics •  criminal justice •  fingerprint analysis •  wrongful conviction •

In the hushed silence of a courtroom, every word and piece of evidence carries immense weight. Picture the scene: attorneys meticulously lay out DNA matches, eyewitness accounts, and other critical evidence, each piece scrutinized and debated in the pursuit of truth. In this setting, probability theory and statistics emerge as invaluable allies. They transform from abstract mathematical concepts into practical tools that guide the hands of justice, ensuring that decisions rest on a solid foundation of logical reasoning and data analysis.

My experiences have provided me with a unique perspective on these matters. In 2011, I was appointed to the Board of Appeals for Howard County, where I examined the nuances and complexities of cases ranging from conditional uses to appeals against decisions made by county agencies. The board’s responsibility to meticulously examine testimonies and evidence underscored the vital role that precision and thorough analysis play in the legal process. Ensuring justice is not just about having evidence but also about interpreting it correctly, and mathematics provides us with the tools to do just that.

In 1999, the Sally Clark case brought this issue to the fore. Sally Clark, a solicitor and mother, was wrongfully convicted for the deaths of her two infant sons. The conviction heavily relied on the testimony of Sir Alan Roy Meadow. This pediatrician stated that the probability of two affluent siblings from an affluent family dying of sudden infant death syndrome (SIDS) was 1 in 73 million. However, this calculation was grievously flawed. It failed to account that the deaths were not independent events, and the actual probability was closer to 1 in 200. Subsequent review and statistical analysis led to Clark’s exoneration in 2003, but the case underscored the potential for tragic errors when statistical data is misinterpreted.

A similar miscarriage of justice occurred in 2003 with the case of Lucia de Berk, a Dutch nurse. De Berk was convicted of multiple murders based on a statistical analysis of her frequent presence during patient deaths. The probability calculation, which suggested an extreme unlikelihood of mere coincidence, was later revealed to be fundamentally flawed. De Berk was exonerated in 2010 after a re-examination of the evidence and statistics.

These cases serve as sobering reminders of the profound impact that statistical analysis can have on individuals’ lives. They underscore the necessity for accurate, careful statistical work and highlight the potential consequences when it is misunderstood or misapplied in a legal context.

Forensic evidence, including DNA and fingerprints, often plays a crucial role in legal proceedings, providing seemingly concrete links between individuals and crime scenes. However, applying probability theory is paramount to accurately interpret this evidence.

DNA profiling examines specific regions in a DNA sequence, with samples being compared to determine the likelihood of a match. The uniqueness of these sequences in an individual allows for highly precise identification. In many cases, such as the infamous O.J. Simpson trial of 1995, DNA evidence has been pivotal. Here, despite a strong DNA match connecting Simpson to the crime scene, the defense argued that contamination and mishandling of evidence affected the reliability of the DNA analysis.

Similarly, fingerprint analysis relies on probability to match prints found at crime scenes to individuals. By comparing minutiae points—unique features in the ridge patterns of fingerprints—analysts estimate the likelihood that the prints belong to the same person. While fingerprints have been used for over a century in forensic science, they are not infallible. Errors can arise from partial prints or poor-quality samples, making statistical rigor crucial to prevent misidentification.

Bayes’ Theorem, a principle of probability theory, allows for the updating of the probability of a hypothesis based on new evidence. In a legal context, it can be applied to assess the probability of guilt given new evidence. For instance, consider a case where a suspect’s DNA is a partial match to evidence from a crime scene. Bayes’ Theorem can be used to calculate the likelihood of the suspect’s guilt, considering the partial match and the rate of such matches in the general population.

Understanding and accurately applying probabilistic reasoning in interpreting forensic evidence is crucial for ensuring justice. These mathematical tools provide a way to quantify uncertainty and make informed decisions based on incomplete or ambiguous data. While statistics and probability theory can be powerful tools in the legal system, they are not without their pitfalls. Misuse or misunderstanding statistical data can lead to controversial and sometimes unjust decisions.

Several cases have highlighted the consequences of misinterpreting statistical data. For instance, the Sally Clark case, previously mentioned, is a stark example where misapplication of probability led to a wrongful conviction. In this case, the failure to correctly apply conditional probabilities and consider dependent events resulted in a tragic error. Certain statistical methodologies, especially those involving conditional probabilities or large datasets, can be particularly prone to misinterpretation. The misunderstanding often arises when complexities of real-world data clash with the assumptions made in statistical models.

One common error is the “Prosecutor’s Fallacy,” where the probability of observing certain evidence given a person’s innocence is confused with the probability of a person being innocent given the observed evidence. For instance, in the case of People v. Collins (1968), a couple was convicted of robbery based on a prosecutor’s argument that the likelihood of a coincidental match of their distinctive attributes—race, hair color, etc.—was extremely low. However, this confused the probability of randomly selecting a couple with those features with the likelihood of their guilt. The fallacy lies in failing to consider how many such couples existed and could have committed the crime.

These instances underscore the need for careful application and interpretation of statistical data in legal contexts to avoid such fallacies and ensure fair and accurate judgments. Correctly interpreting and applying probability is crucial in ensuring that justice is not only served but is rooted in a bedrock of sound logical reasoning and empirical analysis.

Legal professionals and statisticians must engage in continuous dialogue and collaboration to refine the interpretation of evidence. This synergy reflects the detailed scrutiny and nuanced understanding I observed while serving on the Board in Howard County. Continuous education and heightened awareness of statistical methodologies among legal professionals are paramount to avoid missteps and ensure the responsible application of these powerful tools.

We can envision a future where our legal system adeptly wields mathematical tools, yielding fair, informed, and just outcomes. By fostering a culture of learning and vigilance, we can ensure that statistical reasoning is an ally, not an adversary, in pursuing justice.