Probability and mass shootings

E. Fuller Torrey writes,

there are now some one million people with serious mental illness living among the general population who, 60 years ago, would have been treated in state mental hospitals. Multiple studies have reported that, at any given time, between 40% and 50% of them are receiving no treatment for their mental illness.

He blames de-institutionalization for the problem of mass murders.

Ordinarily, I try to avoid commenting on the stories that dominate the news for short periods of time. I have a lot of doubts about going ahead with this post, but here goes.

I have a problem with every policy proposal that I have seen for dealing with mass shootings. The problem comes from Bayes’ theorem, which says that the probability of A given B is not the same as the probability of B given A.

When I taught AP statistics, I often used the 9/11 attacks as an example. Nearly all of the terrorists were Saudi nationals. But only a tiny percentage of Saudi nationals are terrorists. So a policy based on the assumption that Saudi nationals are the problem is going to involve a lot of costs relative to potential terrorist acts prevented.

The same thinking applies to guns. Guns account for 100 percent of mass shootings. But only a small percentage of guns are involved in such shootings. If guns provide a benefit to the people who do not use them for mass shootings, then trying to get at mass shootings by going after guns is going to involve a high ratio of costs to benefits.

The same probabilistic reasoning also applies to mental illness. Suppose that people with untreated mental illness account for 100 percent of mass shootings. There are still half a million untreated mentally ill who are not mass shooters. If the cost of mandatory treatment for them is high, then that may not be a good strategy for trying to reduce mass shootings.

Perhaps there are other social benefits to forced institutionalization of those who are mentally ill. That might improve the benefit/cost analysis for such a policy. But even so, it would be difficult to defend from a humanitarian or libertarian viewpoint.

As long as mass shootings remain rare relative the causal factors that are most often cited, it will be hard to come up with a cost-effective solution. This RAND meta-analysis supports my view.

Ben Thompson writes,

it was on 8chan — which was created after complaints that the extremely lightly-moderated anonymous-based forum 4chan was too heavy-handed — that a suspected terrorist gunman posted a rant explaining his actions before killing 20 people in El Paso. This was the third such incident this year: the terrorist gunmen in Christchurch, New Zealand and Poway, California did the same; 8chan celebrated all of them.

Hence, he supports censorship of 8chan. I disagree, although I find it a close call. My thoughts:

1. Correlation does not imply causation. The fact that terrorists were active on 8chan could mean that 8chan attracts individuals who are inclined toward violence, but it does not necessarily increase their propensity toward violence.

2. As a test, you may substitute “radical Islamic preacher” or “Palestinian primary school that teaches kids to hate Jews” for 8chan, and see whether you support the step of absolutely shutting down their right to speak. Maybe you do. I do not.

3. Probably the most effective way to use censorship to reduce mass shootings would be to refuse to allow the media to cover them. As it is, the mainstream media are giving mass shooters the notoriety that seems to be their main motivation. Sometimes there are suggestions that the media voluntarily exercise restraint, for instance in not naming the shooter. But as far as I know nobody wants to impose censorship on the mainstream media, even though they appear to be at least as guilty of aiding and abetting mass shooters as are the dark-web media.

4. Ultimately, censorship gives power to the censors. As time passes, the trend will be for censors to exercise more and more power with less and less wisdom, objectivity, and discretion. I think it is best to stay off the slippery slope altogether.

UPDATE: a commenter points to a very similar post by Craig Pirrong, aka the Streetwise Professor. Note that the first comment on that post repeats my point 3.

28 thoughts on “Probability and mass shootings

  1. There are so many issues entwined in this wicked problem. Two examples.

    One: any system which is designed primarily to prevent tail events… ends up placing a very heavy burden on the rest of the system.

    Two: completely different experiences and perceptions of governments and weapons. For some people, basically every government they hear about is oppressive and violent. For others, the government is the source of protection.

    Same with guns, generally reversed.

  2. I’m willing to endure some number of deaths in exchange for gun ownership and no police state. Not every problem has a (tolerable) solution.

  3. We don’t need to take the logical approach applied here.

    There are two classes of issues to consider.

    First, what are the firepower limits of the second amendment rights? If the continuum is from a musket to a shoulder launched anti-tank missile, where do you draw the line and how?

    Second, does the state have any right to restrict the use of weapons for certain high risk persons or not? We can stipulate due process, which is critical.

    What of citizens who a court of law has found to have been guilty of an act of violence, or guilty of threatening someone with an act of violence?

    Can the state suspend the right to bear arms to someone who a court has deemed not compos mentis?

    Do we allow or even require a court to issue a suspension of gun rights, pending explicit reinstatement? Do we allow law enforcement to confiscate weapons?

    • “If the continuum is from a musket to a shoulder launched anti-tank missile, where do you draw the line and how?”

      From what I understand, many legal thinkers currently draw the line at “guns commonly owned for lawful purposes”. The “commonly owned” standard has the advantage of allowing us to harness distributed, localized information possessed by gun owners about the useful features of various guns for lawful purposes.

      For example, I believe that the AR-15 is the most popular rifle in America. In terms of an arm commonly-owned by everyday citizens, it would seem to fall closer to a musket than an anti-tank missile. Personally, I don’t know much about guns, but that’s what I have gleamed from listening to law-abiding gun enthusiasts.

      • You don’t see a logical problem in this argument? Your explanation describes a line, but also defines the line as a floating standard defined by gun owners. They can’t define the line and be bound by the line at the same time. You are describing no line at all.

        • That’s common in Constitutional law.

          Consider the Fourth Amendment standard from Smith v Maryland (1979), which requires that:

          (1) a person “has exhibited an actual (subjective) expectation of privacy”; and
          (2) society is prepared to recognize that this expectation is (objectively) reasonable.

          That “society” part is most definitely a floating standard, that is, “no line at all” in your sense, and not just a movable public “consensus”, but indeed, only what some judges are willing to claim is the public consensus, which, true or false, is good enough so long as the higher courts want to go along.

          The trouble is that the right is protection from unreasonable searches and seizures, but what’s ‘reasonable’? Actually, that question isn’t really important. The important question is always, “Who gets to say?”

          And it’s not just for the Amendments which have the word ‘reasonable’ in them, which some argue has a clear intention and implication of granting the judiciary flexibility in exercise of interpretive power.

          But what the judges have done with the the various levels of ‘scrutiny’ needed to overcome Constitutional limits is really the same thing. What’s ‘compelling’ enough? To whom? When is the tailoring ‘narrow’ enough? Which rights get which ‘level’ of scrutiny?

          It only takes a little wiggle room to give The Devil enough air to thrive and work his mischief. How do you police all these discretionary judgment calls so that judicial power isn’t abused? You can’t.

        • It’s analogous to the “prevailing community standards” test for obscenity. History, custom, and tradition plays an important role throughout our common law system. In the case of gun control, where we are weighing the potential benefit of keeping guns out of the hands of people that might later use those guns unlawfully against the cost of denying people the right to own guns for lawful purposes, it would seem relevant how common it is for people to own a particular gun for lawful purposes.

        • Handle/BC

          You are describing laws addressing standards of behavior, non-physical personal accommodations, and social constructions, which cannot be constrained in advance, with the legality of physical products with objective specific physical traits, which can.

          There is a valid argument to be made that coming up with language that will provide the right balance of concerns will be difficult. But “commonly owned for lawful purposes” bakes in an assumption of tolerance for “uncommonly owned for lawful purposes”.

          We cannot always draw a clear line with the law. The question is whether we can here or not.

  4. Honestly, I think the worst solution here is more guns and Red state mandates to increase gun carrying onto private property.

    1) While gun sales have increased, gun ownership is decreasing across the nation. This is long good thing as less gun owners, the less gun deaths. And if private property does not want guns, I think it should be their to do so. I don’t want to carrying at a church or Wal-Mart. (And how is it good that Wal-Mart allows people with guns in the store?)

    2) Probably the best point by Steve Sailer about the increase mass gun shootings is the decline of serial killers. These don’t happen much anymore.

    3) Gun deaths have decreased over the last several decades from lot of single or two deaths. Gun deaths at school are a lot less than decades ago.

    4) Oddly enough, the only time I start supporting gun control is listening to Wayne Lapierre. Good society does not need more guns.

    5) The only gun control I like is needing insurance for a gun purchase much like car insurance. So legally owning lots of guns or AR-15 are a lot more expensive in the market. (And gun insurance won’t stop all mass gun shooting but it could mitigate by making a lot more expensive to buy and own this stuff. And Black market gun sales around insurance will be more expensive.)

  5. The solutions to decrease spree killings tend to fall under three categories, all regulatory:

    1. weapon regulations
    2. mental illness regulations
    3. speech regulations

    There is enough regulatory diversity in the Anglosphere and the EU and enough incidents throughout these nation-states to make good rough-estimates (Fermi estimates?) of the efficacy of each proposed policy. I think Kling is correct in his assessment that the current set of regulations being proposed are unlikely to achieve positive benefits if honestly and carefully analyzed.

    Most of the discussions, especially from politicians, are about signalling.

  6. “As a test, you may substitute ‘radical Islamic preacher’ or ‘Palestinian primary school that teaches kids to hate Jews’ for 8chan”

    Why stop there instead of widening the circle to include *popular* groups? Should criticism of Republicans be suppressed because of the guy that tried to assassinate Congressional Republicans? One hundred percent of mass killers have been humans. Does that mean we need to get all humans off the street? If not, why not?

    • I assumed that Palestinians were supposed to be a popular group in this scenario (on the left).

  7. Is there any evidence that either of the two recent U.S.-based shooters or the one in NZ would have been candidates for involuntary commitment?

    • Neither the El Paso shooter or the New Zealand shooter appears to have been a lunatic absent the murderous acts themselves. I find it almost impossible to believe that either one could have been held for mental illness reasons prior to those acts. The Dayton shooter is closer to what you would expect to find for a lunatic, but even there the man was socially functional and I doubt any court could have had him held for very long.

  8. Behavioral contagion (or “social contagion”) is a real and terrible thing. See also “Rapid Onset Gender Dysphoria”, which, like suicides, tends to occur in clusters according to popular and peer influences.

    In debates about Libertarianism and where one might permit the exercise of state power against the individual, one hypothetical that comes up is the quarantine power in the case of contagious disease, which usually brings up the ‘Typhoid Mary’ case. And what about banning imports or immigration from countries with certain invasive pests or dangerous epidemics?

    But little thought has gone into what can or ought to be done about socially contagious dangers, or whether it is even lawful or compatible with anti-discrimination principles for groups to quarantine themselves against perceived negative influences.

    • But little thought has gone into what can or ought to be done about socially contagious dangers…

      I think there has been a great deal of thought about curbing socially contagious dangers; no effective solutions have emerged but a great deal of thought has occurred.

  9. My home in the southern hemisphere is a place that has tight gun laws. However, it also allows its citizens to protect themselves. My home has a corten steel door, windowless 3 meter concrete walls around the perimeter which are topped with electrified barbed wire. The exterior is frequently tagged with graffiti but it is in a relatively nice neighborhood going beyond the superficial appearances that are often jarring to US visitors. But I feel safer there than I do in my Northern Virginia home.

    With single family zoning slated for elimination, people in the US will all be living in neighborhoods populated by people you simply don’t know and have no idea as to whether you like them. Science has demonstrated that such neighborhoods have increased rates of crime and lower levels of trust. Since I have clinical depression I decided to give away my weapons years ago and when in the US have been free-riding on my armed neighbors. Their gun ownership has greatly decreased the probability that I will be attacked and robbed by home invaders. I am grateful to them for owning guns. Potential malefactors have no way of knowing in which homes they will be greeted with gun fire, so I am less likely to be a target.

    If gun protection is eliminated, criminals will face much less deterrence. Crime rates and murders will increase. Perhaps significantly. If guns go, it is incumbent upon local zoning boards to allow local residents to respond appropriately and fortify their homes. 12 foot concrete perimeter fences will save many lives. Failure to allow people to so reasonably protect themselves while stripping firearm protections is tantamount to genocide.

    • I’m surprised by the degree of self-disclosure that occurs in these comments. It certainly adds to the conversation but I don’t think I have the confidence to do the same [end of aside].

      The firearm owners I know in Canada and Australia do not think of their guns as a means of protecting their home/family, unless you consider putting down rabid animals self-defence. Perhaps my sample size is too small or skewed towards hunters (with long guns) but many of them are immigrants from low-trust societies so I’m confused.

      So my question is, why are the U.S. and Brazil so different than Canada, Australia, and New Zealand? Is the difference part of the development/history of each nation or can established nations change in terms of real and perceived threats?

      • David Kopel wrote an interesting book comparing several distinct national cultures & their treatment of the gun issue: “The Samurai, the Mountie, and the Cowboy.”
        https://amzn.to/2Tx9xQJ
        It was published in 1992, so has pretty old stats in it; I’d love to see him update it.

  10. The same probabilistic reasoning also applies to mental illness. Suppose that people with untreated mental illness account for 100 percent of mass shootings. There are still half a million untreated mentally ill who are not mass shooters. If the cost of mandatory treatment for them is high, then that may not be a good strategy for trying to reduce mass shootings.

    Perhaps there are other social benefits to forced institutionalization of those who are mentally ill. That might improve the benefit/cost analysis for such a policy. But even so, it would be difficult to defend from a humanitarian or libertarian viewpoint.

    It’s *easy* to defend this from a humanitarian viewpoint. Because the alternative – what we have now, is not humane. Living on the street with no real support services, surrounded by other mentally ill people of various propensities to random violence, is a pretty inhumane policy. It probably also kills more people than mass shootings do. Nothing else that liberals and libertarians have tried since the emptying of the mental asylums in the 1960s has worked, and it’s imposed huge social and financial costs on the overall community while drastically lowering the life expectancy and quality of life of the mentally ill.

    So even if it doesn’t prevent *any* mass shootings, restoring involuntary confinement of those people too mentally ill to take care of themselves, is worth doing.

    • Indeed. “Lock them up to prevent mass shootings” is indeed an idiotic solution to a non-problem borne of statistical ignorance.

      “Commit them to institutions because having San Fran spend $100,000 per homeless person accomplishing nothing and causing huge problems for residents when really the problem is a large portion of them are mentally ill people that should be institutionalized” is a rational argument that makes statistical sense and could have a meaningful impact.

      It’s the same with many other things. You don’t support an immigration bad from a country because of terrorism. You support it if the average immigrant from that country isn’t a net positive for the host country, and that’s an easy enough to interpret and enforce metric to be used at scale. Even if there was zero Islamic terrorism in Europe, it would still be a good idea to cut immigration from the Middle East.

      I don’t think there is much to learn from these things on the ideological front. The shooters all have differing “ideologies” both between themselves and even within themselves. They change their minds about what they believe constantly, and have a very shallow understanding of whatever it is they claim to believe the day they go on a spree.

      “Social outcast loser engaging in what amounts to a spectacular assisted (by the police) suicide” seems the most apt description of them all. In a different context maybe they would jump off a building or in front of a train to get attention.

      The only way you’re going to get less of these shootings is to have fewer losers in your society, and to have being a loser be less of a miserable thing for them. But that is expensive and requires trade offs that we haven’t been willing to make for a variety of reasons. Instead we’ve got a lot of suggestions as to how to manage our growing loser problem so they are still there and miserable but maybe they don’t go on a shooting spree. It’s very treat the cause not the disease.

      • You don’t support an immigration bad[/ban] from a country because of terrorism. You support it if the average immigrant from that country isn’t a net positive for the host country, and that’s an easy enough to interpret and enforce metric to be used at scale.

        Careful Icaraus, people who live in glass houses shouldn’t brandish net positives. I’m sure the people of El Paso and Christchurch do not think people with white-nationalist sentiments are a net positive. I’m assuming the opposite is true especially in Christchurch where the gunman was an Australian national.

        If you believe Islamist sympathies are enough to deny entry at a border then white-nationalist sentiment shouldn’t be far behind. Domestic terrorism has many forms.

        • I’d be interested to know, how many identifiable white supremacists enter the United States from foreign countries each year? What is the attitude of the US immigration authorities to applications from people espousing such views? How much white supremacist activity within the US is conducted by recent immigrants?

          If we’re admitting significant numbers of immigrants who advocate for white supremacy (as opposed to just being white) – by all means, let’s stop!

    • The argument for involuntary institutional commitment for mental illness assumes that such institutions are both humane and effective. I think this is not universally the case. My evidence is Western State Hospital in Washington State, which descended into such corruption and inhumanity that it lost its federal subsidy. The history of government-run mental institutions is rife with horrors, some of which my older brother endured. Moreover, if you sweep up 10,000 allegedly mentally ill, how many of those are potential murderers? Won’t we just be subjecting those who are not violent to the violence of those who are?

      • Is your local badly-run mental hospital so bad that it’s better to live under an overpass, getting beat up for begging in the wrong spot, hoping you don’t get robbed or killed in your sleep, being unable to clean yourself or your clothes for weeks at a time, and taking street drugs of unknown quality and safety to endure it all?

        Because that’s the *real* tradeoff.

        Sure – state-run mental hospitals *should* be well-run and humane places. but all institutions will fail now and then. But that failure generally looks less bad than the current failure.

        • By that standard, prison is just as good of an alternative to a mental health facility. I think that’s the trade off we’re making today.

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