Australia’s Gun Control Laws Probably Worked

There’s an odd article in the Washington Post by Leah Libresco, formerly of 538, that says:

I researched the strictly tightened gun laws in Britain and Australia and concluded that they didn’t prove much about what America’s policy should be. Neither nation experienced drops in mass shootings or other gun related-crime that could be attributed to their buybacks and bans. Mass shootings were too rare in Australia for their absence after the buyback program to be clear evidence of progress. And in both Australia and Britain, the gun restrictions had an ambiguous effect on other gun-related crimes or deaths.

The work referenced says:

Did Australia and Great Britain’s reforms prevent mass shootings? It’s hard to say, simply because mass shootings are relatively rare. In the post-buyback period, Great Britain has had one massacre with guns while Australia has had none. It’s hard to calculate how many would have been expected without a ban. Australia looks more successful in this regard, because it had more frequent mass shootings before the ban (averaging about two mass shootings every three years from 1979 to 1996.3) Mass shootings in Great Britain, prior to the ban, were rarer. Prior to 1996, there hadn’t been a widely covered mass shooting in Britain since 1987.

I don’t know Libresco’s background or education. Working for 538 suggests a basic competency, but the notion that “it’s hard to calculate how many would have been expected without a ban” is a frankly bizarre statement.

I’m a physicist who has worked in various areas of physics, medicine, and biology over the past 30 years. Working with biologists, in particular, has been an education in how to handle small datasets. If I had a dollar for every time a biologist has come to me and wanted to know if there is a significant difference between their control and experimental samples when they have one of each I could easily buy a coffee at Starbucks.

It’s not that hard to deal with such cases using prior information, and the Australian dataset on mass shootings is postively overflowing in comparison. The Great Wiki gives us dates and numbers dead for Australian mass shootings in the modern era:

# date, #killed (only 4 or more indiscriminate victims included)
#1984.75,7 # gang shootout => not indiscriminate
#1993.25,5 # ended in hostage incident => not indiscriminate

I have eliminated arson attacks, as gun control seems unlikely to have an effect on them, and applied the rule of thumb used by the US Congressional Research Service, which defines a “mass shooting” as: “one in which four or more people selected indiscriminately, not including the perpetrator, are killed, echoing the FBI definition of the term ‘mass murder’.”

There are many ways to turn this incredibly rich dataset into an estimate of the plausibility that the 1996 gun ban is responsible for the absence of mass shootings since 1996. The way I have chosen is to look at the distribution of intervals between mass shootings between 1971 and 1996. Generating a histogram with 1 year bins, the data look like this:

Intervals between mass shootings in Australia between 1971 and 1996

The exponential fit to the data is justified by the assumption that mass shootings are uncorrelated with each other and therefore described by a Poisson process, since the intervals between Poisson process events have an exponential distribution. The fit has a lifetime of 1.74505 years between shootings. The fit quality is quite good, with a reduced χ2 of less than 1.

But remember, all this is hard. So hard we have to use two whole lines of Python to estimate the probability that it has been more than 20 years since the last mass shooting in Australia just by random chance:

from numpy.random import exponential
print(sum([x > 20 for x in exponential(1.74505, 100000000)])/100000000.0)

I’m just doing something brutally simple here to make a point: it isn’t really that hard at all.

The result is that the probability is almost exactly 10-5–a one in a hundred thousand chance–that the current interval between mass shootings in Australia is due to chance alone.

It is reasonable to infer that the changes in gun laws had an effect, particularly because we as good Bayesians know that if you make something desirable easier to do, more people will do it.

Killing is desirable to a lot of people. The most common causes of murder in the US are relatively trivial interpersonal slights. We monkeys get angry, and when there is a machine that makes killing really, really easy near at hand we have a tendency to use it.

If guns didn’t make killing really, really easy they’d hardly be any use against criminals, so anyone who argues otherwise is saying there is not value in protecting gun ownership because they are kind of useless machines anyway.

Killing is desirable and easy access to guns makes it easier, so where there are more guns, there is more killing. Conversely, fewer guns, especially fewer guns of the right type, leads to less killing. It would be bizarre in the extreme if it were otherwise, and the data from Australia is fully consistent with these facts.

It may be there are other factors at work in Australia, but opponents of gun control will have to positively identify another cause for the extremely long interval between mass shootings that Australia has experienced since limiting access to firearms if they want to make the claim that gun control has not worked there.

About TJ

Scientist, engineer, inventor, writer, poet, sailor, hiker, canoeist, father.
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