This brief essay from December 2015 [1] presents the hypothesis that social environments and psychological distributions lay behind the observed frequency of mass shootings. I've considered updating and expanding it following many of the atrocious mass shootings over the intervening years [2]. Perhaps at some point I will. In the meantime, I hope that posting it – naiveites included – will spur research linking improbable individual actions to populations and the social environment.
Mass shootings are virtually impossible to accurately predict. The most we can say is that one rampage shooting occurs somewhere in the United States, on average, every day [3]. The rate and magnitude of such acts have generally increased over the past few decades [4], but different data sources provide very different figures. Whereas between 2000 and 2013 the FBI records 160 incidents, the Mass Shooting Tracker lists 363 in 2013, 336 in 2014 and 353 so far in 2015. Shootings also have a financial cost. Estimates of the total annual cost of gun violence exceed $200 billion [5] or about 1.5% of GDP. For many varied and complex reasons such tragic events are often front-page news—and they are likely to continue to be so for years to come.
Our understanding of mass shootings is largely based on investigation after the fact and through interpretation of trends in incidence, injuries and deaths. The central issue frustrating prediction is that these events are too rare for statistics to say much about when and where they may happen. This is because although mass shootings appear frequently in the news, they are perpetrated by extremely small numbers of people. Consider that in 2015, about 1 person in 1 million in the United States was an aggressor in a mass shooting. Because of the complex and idiosyncratic circumstances leading to many shootings (the dynamic state of mind of the person, and (possibly sudden) changes in the environment sparking the event), a predictor would require orders of magnitude more screening for red flags than the actual numbers committing these acts to have a reasonable chance at lowering future incidence. This poses a considerable challenge in information-gathering and pursuing leads, without compromising basic liberties and freedoms.
Importantly, if the probability distribution of risk in perpetuating a mass shooting based on one or more indicators follows a bell-shaped curve, and is slowly either being inched in the direction of rampage violence, or the shape of the distribution is differentially shifting towards the high-risk tail, then we may well see drastic increases in mass shootings in the not too distant future. This is because the number of people at any given risk level increases
exponentially as we go from the tail towards the center of a bell-shaped curve. Reasons for a statistical shift include greater numbers of firearms and assault weapons held by citizens (that is, more means), and elusive, complex changes in society towards the expression of this form of violence. Importantly, we simply don’t know the shape of the risk-of-rampage distribution. We expect—and hope—that it is very highly skewed towards zero probability. However, due to the sheer size of the population, even very small probabilities that individuals at or near the high-risk tail will act, mean that mass shootings appear to be here to stay as long as people have firearms.
Governments and citizens react to the news of mass shootings through attempts at better prevention and protection. What transpires is metaphorically akin to an arms race: shooters act, governance reacts with novel or augmented defense and information gathering, the common citizen arms himself [6], shooters-to-be overcome defenses or find softer targets, and so on ad infinitum. This dynamic is particularly evident in terrorist mass shootings. The November 13th attacks in Paris show that criminals can find refuge in European countries that are relatively permissive to firearms and the risks of terrorism, and exploit the Schengen Agreement by freely and legally crossing national boarders to perpetrate their acts. In reaction, both French and Belgian governments are attempting to crackdown on individuals or groups perceived as future threats [7]. Following the December 2nd San Bernardino shootings the FBI is investigating what predictive clues may have been missed [8], undoubtedly to prevent such events from happening in the future. In these and other cases governments want to show both citizens and would-be terrorists that they are reacting, but don’t want to reveal too much about how, for fear that terrorists will counter-adapt [9]. Signals and motives are important in fueling terrorism and its escalation, and this has been compared to kinship in natural systems, such as the frequent observation of self-sacrifice when colonies of social insects such as honeybees perceive that they are threatened by attack [10].
Mass shootings are a new normal. That is, the problem at hand is not sufficiently threatening compared to difficulties, real or perceived, in addressing it. Outcry that could foster a change may unfortunately only happen should the numbers of these events increase staggeringly, or if there is one cataclysmic event resulting in significantly more victims than ever before. Either way, concerted action in prevention will need to enter the news before we can hope that mass shootings find their way out.
[1] Submitted to Edge on December 13th, 2015, and rejected because it was not “scientific news”
[2] Recent world trends can be found at https://www.bbc.com/news/world-us-canada-41488081
[3] http://www.shootingtracker.com/wiki/Main_Page
[4] https://www.fbi.gov/news/stories/2014/september/fbi-releases-study-on-active-shooter-incidents/pdfs/a-study-of-active-shooter-incidents-in-the-u.s.-between-2000-and-2013. http://www.motherjones.com/politics/2014/10/mass-shootings-increasing-harvard-research
[5] http://www.motherjones.com/politics/2015/04/true-cost-of-gun-violence-in-america
[6] http://nyti.ms/1SPMnxk
[7] http://www.gouvernement.fr/conseil-des-ministres/2015-11-18/la-reponse-aux-attentats-terroristes
[8] https://www.fbi.gov/news/testimony/oversight-of-the-federal-bureau-of-investigation-8
[9] Sagarin et al. 2010. Decentralize, adapt and cooperate. Nature 465: 292-293
[10] Blumstein et al. 2012. “The peacock’s tale: Lessons from evolution for effective signalling in international politics”. Cliodynamics: The Journal of Theoretical and Mathematical History 3:191-214.