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Tackling gun violence: is systems thinking necessary?

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Abstract

Gun violence is a global epidemic claiming thousands of lives every year. In the United Stated alone, almost 25,000 lives are lost every year due to gun-inflicted suicides. In this paper, we argue for an inclusion of systems thinking methodologies in tackling gun violence. As a first step of an inductive reasoning approach, we illustrate the pitfalls of traditional reductionist methods, by analyzing open-source data collated in the United States by the Federal Bureau of Investigation. The specific goal of this exploratory risk analysis is estimating the probability of a police officer being feloniously killed during an incident. We explore the correlations between factors such as police department size and demographics with the probability of an officer being feloniously killed. Using similarity measures, we also benchmark the performance of police departments, to compare them to other similar sized departments. Our exploratory analyses indicate that a critical officer ratio of 5 officers per thousand population covered could lower the probability of police officers being feloniously killed. Moreover, the total number of female police officers, as a percentage of a department’s force, needs to be increased. Via this process of risk estimation, we identify various difficulties that confound traditional operational research methodologies, arguing for the inclusion of a systems thinking toolkit to tackle gun violence. In particular, dovetailing traditional OR with a soft systems methodology (SSM) may be needed to tackle gun violence effectively.

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Acknowledgements

Support from the New Jersey center on gun violence for this project is gratefully acknowledged. The Center on Gun Violence Research works in collaboration with and is supported by New Jersey’s Office of the Secretary of Higher Education (OSHE).

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Correspondence to Ram Gopalan.

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Appendix: Statistical tests

Appendix: Statistical tests

1.1 Impact of officer rate (workload) on P-FK

Data on officer fatalities were extracted from LEOKA (Law officers killed or attacked), an open-source data set collated by the FBI for a five year period 2012–2016. The monthly numbers were aggregated to a yearly total. For a department-year to be a valid record, the record must contain information for both the population covered (workload) as well as the number of officers in that department for that year. Data was available for a total of 75,058 department-years, which were placed in two buckets: those departments with a critical officer ratio per thousand population = CR >  = (a threshold), or CR < threshold. (see Sect. 4.1 for a definition of this critical ratio). In this appendix, we show results for two values of CR: CR = 0.004, CR = 0.005. P-FK, the proportion of departments with an officer fatality were compared for the two buckets as per the hypotheses below:

H0

P-FK(CR >  = threshold) ≥ P-FK(CR < threshold).

H1

P-FK(CR >  = threshold) < P-FK(CR < threshold).

Let p1 = P-FK(CR >  = threshold), p2 = P-FK(CR < threshold) and p = pooled proportion of department-years when a department experiences a fatality (i.e., P-FK for both buckets together).

σ = \(\sqrt{p(1-p)(\frac{1}{n1}+\frac{1}{n2})}\), where n1 = number of departments with CR >  = threshold and n2 = number of departments with CR < threshold. The test statistic Z = (p1 – p2)/ σ. (see Anderson et al. [32], chapter 10 for details of the test). For a one-tailed test and α = 5%, the critical value Z-critical = − 1.64.

1.1.1 A1.1 CR = 0.004

 

# departments with no fatalities

# departments with a fatality

TOTAL

CR < 0.004

68,570

156

68,726

CR ≥ 0.004

6321

11

6332

Total

74,891

167

75,058

For the data above, p1 = 0.00173, p2 = 0.0023, p = 0.00223, σ = 0.00062 and Z = 0.86 and the p-value = 0.195. The effect of department size is not significant for α = 5%.

1.1.2 A1.2 CR = 0.005

 

# departments with no fatalities

# departments with a fatality

TOTAL

CR < 0.005

71,225

164

71,389

CR ≥ 0.005

3666

3

3669

Total

74,891

167

75,058

For the data above, p1 = 0.000818, p2 = 0.002297, p = 0.002225, σ = 0.000798 and Z = -1.85 and the p-value = 0.03. The effect of department size is significant for α = 5% when CR = 0.005. Some analysts prefer that np ≥ 5 in all cells for this test. Given that only 3 departments had any officer fatalities when CR ≥ 0.005, we tested the above hypothesis using a normal approximation to binomial probabilities. For this alternate test, we assumed a base binomial probability of p2 = 0.002297 (equivalent to the situation when CR < 0.005). Using this p2, we computed the probability of 3 or fewer fatalities for 3669 binomial trials (= number of departments with CR ≥ 0.005), using a normal approximation to binomial probabilities. The odds of this occurrence is 0.0306 (equivalent to the p-value in the hypothesis test above).

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Gopalan, R., Lin, T. Tackling gun violence: is systems thinking necessary?. OPSEARCH 59, 908–929 (2022). https://doi.org/10.1007/s12597-022-00577-1

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