The assumption of fingerprint uniqueness is foundational in forensic science and central to criminal identification practices. However, empirical evidence supporting this assumption is limited, and recent findings from artificial intelligence challenge its validity. This paper uses a probabilistic approach to examine whether fingerprint patterns remain unique across large populations. We do this by drawing on Francis Galton's 1892 argument and applying the birthday paradox to estimate the probability of fingerprint repetition. Our findings indicate that there is a 50\% probability of coincidental fingerprint matches in populations of 14 million, rising to near certainty at 40 million, which contradicts the traditional view of fingerprints as unique identifiers. We introduce the concept of a Random Overlap Probability (ROP) to assess the likelihood of fingerprint repetition within specific population sizes. We recommend a shift toward probabilistic models for fingerprint comparisons that account for the likelihood of pattern repetition. This approach could strengthen the reliability and fairness of fingerprint comparisons in the criminal justice system.

翻译：指纹唯一性假设是法医学的基础，也是刑事鉴定实践的核心。然而，支持这一假设的经验证据有限，且人工智能的最新发现对其有效性提出了挑战。本文采用概率方法研究指纹模式在大量人群中是否保持唯一性。我们借鉴弗朗西斯·高尔顿1892年的论点，并应用生日悖论来估计指纹重复的概率。研究结果表明，在1400万人口中，偶然性指纹匹配的概率为50%，当人口达到4000万时，匹配概率接近确定性，这与将指纹视为唯一标识符的传统观点相矛盾。我们引入随机重叠概率（ROP）的概念，以评估特定人口规模内指纹重复的可能性。我们建议转向考虑模式重复可能性的指纹比较概率模型。这种方法可以增强刑事司法系统中指纹比较的可靠性与公平性。