Dependence of the Firearm-Related Homicide Rate on Gun Availability: A Mathematical Analysis

In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data.

在美国，枪支的合法可获得性与涉枪凶杀率之间的关联一直存在争议。有观点认为，无限制的枪支可获得性会加剧枪支引发的凶杀案件的发生；也有观点指出，遭遇袭击时持有枪支可保护潜在受害者。本文首次对这一权衡关系开展数学分析，旨在引导这场争论聚焦于假设、统计数据与科学方法的探讨。本模型基于一系列明确定义的假设，这些假设均有现有统计数据支撑，且采用公理化形式构建，确保所得结果不会依赖于任意设定的数学表达式。依据该分析框架，存在两种可使涉枪凶杀率降至最低的备选方案：一是禁止私人持有枪支，二是允许普通民众携带枪支。尤为重要的是，本模型明确了决定哪种政策可将死亡率降至最低的关键参数，从而可为未来流行病学研究的设计提供指导。需测量的参数包括：非法持有枪支的罪犯占比、枪支持有所能提供的防护程度，以及选择行使持枪权并在遭遇袭击时携带枪支的人群占比。本文利用现有文献中的有限数据演示了如何对模型进行参数化，该初步分析显示，禁止私人持有枪支，或部分降低枪支可获得性，均有可能降低枪支引发的凶杀率。但鉴于用于模型构建与参数化的数据较为有限，上述结论不应被视为政策建议。不过，本模型明确界定了需测量的内容，为围绕假设与数据开展科学讨论提供了基础。