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

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  • Dominik Wodarz
  • Natalia L Komarova

Abstract

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.

Suggested Citation

  • Dominik Wodarz & Natalia L Komarova, 2013. "Dependence of the Firearm-Related Homicide Rate on Gun Availability: A Mathematical Analysis," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-13, July.
  • Handle: RePEc:plo:pone00:0071606
    DOI: 10.1371/journal.pone.0071606
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    1. Robert L. Helmbold & Allan S. Rehm, 1995. "“The influence of the numerical strength of engaged forces in their casualties,” by M. Osipov," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(3), pages 435-490, April.
    2. Avi-Itzhak, Benjamin & Shinnar, Reuel, 1973. "Quantitative models in crime control," Journal of Criminal Justice, Elsevier, vol. 1(3), pages 185-217.
    3. Lott, Jr., John R., 2010. "More Guns, Less Crime," University of Chicago Press Economics Books, University of Chicago Press, edition 3, number 9780226493664.
    4. Anna Dreber & David G. Rand & Drew Fudenberg & Martin A. Nowak, 2008. "Winners don’t punish," Nature, Nature, vol. 452(7185), pages 348-351, March.
    5. Wright, M.A. & Wintemute, G.J. & Rivara, F.P., 1999. "Effectiveness of denial of handgun purchase to persons believed to be at high risk for firearm violence," American Journal of Public Health, American Public Health Association, vol. 89(1), pages 88-90.
    6. Shah, S. & Grady, C., 2010. "Shah and grady respond," American Journal of Public Health, American Public Health Association, vol. 100(6), pages 967-967.
    7. Branas, C.C. & Richmond, T.S. & Culhane, D.P. & Ten Have, T.R. & Wiebe, D.J., 2009. "Investigating the link between gun possession and gun assault," American Journal of Public Health, American Public Health Association, vol. 99(11), pages 2034-2040.
    8. Helmbold, Robert L., 1993. "Osipov: The `Russian Lanchester'," European Journal of Operational Research, Elsevier, vol. 65(2), pages 278-288, March.
    9. Kennedy, Bruce P. & Kawachi, Ichiro & Prothrow-Stith, Deborah & Lochner, Kimberly & Gupta, Vanita, 1998. "Social capital, income inequality, and firearm violent crime," Social Science & Medicine, Elsevier, vol. 47(1), pages 7-17, July.
    10. Wintemute, G., 2010. "Flaws in study of firearm possession and risk for assault," American Journal of Public Health, American Public Health Association, vol. 100(6), pages 967-968.
    11. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
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    Cited by:

    1. Monteiro, L.H.A., 2020. "More guns, less crime? A dynamical systems approach," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Fu, Feng & Rockmore, Daniel N., 2024. "Too little, too late – a dynamical systems model for gun-related violence and intervention," Applied Mathematics and Computation, Elsevier, vol. 467(C).

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