Monday, 11 March 2013

The Gun Control Debate: A Subject for Game Theory?

There was curiosity after the latest gun-enabled massacre in the States--twenty children and six adults killed in Sandy Hook Elementary School--on how the the National  Rifle Association (NRA) would react. When it did comment, many were surprised by the NRA's proposal that someone with a gun should guard the premises of every school in the United States. The proposal is impractical.

Nevertheless, another group, Guns Save Lives, has gone even further. For them, the solution to criminal shootings is simply to have more guns around. A member explains, "Mass murderers go where they know people aren't armed. One of our goals is to make the number of places where that occurs as few as possible."

To me, and to others, this view seems paradoxical. One does not keep children safe from poisons by making poisons more widespread. One does not even lower the rate of airplane accidents by making sure that more people have airplanes to fly. Logically, if no-one had guns, there would be no gun-enabled killings. One consequence would be (since guns are very efficient killing machines) that fewer people would be killed. This chain of logic seems to be borne out by the facts. Americans have more guns than people in other countries, and they have far, far, more deaths by gunshot.

People on both sides of the argument, I believe, are sincere. Neither side is able to appreciate the other's viewpoint, which makes me think that the difference between the two sides may have very deep roots.Trying to make sense of this, I have turned to Game Theory. Specifically, one of the only aspects of game theory that I understand at all, called the Prisoner's Dilemma.

The original formulation of the Prisoner's Dilemma was this (courtesy of Wikipedia):
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to two years in jail.
So, a year in prison each if both are loyal; zero and three, respectively, if one betrays the other; and two each if both betray. This can be portrayed as a table:

Prisoner B stays silent (cooperates) Prisoner B betrays (defects)
Prisoner A stays silent (cooperates) Each serves 1 year Prisoner A: 3 years
Prisoner B: goes free
Prisoner A betrays (defects) Prisoner A: goes free
Prisoner B: 3 years
Each serves 2 years

I picture the debate over guns in similar terms. An intrusion is taking place, in a home, a workplace, or a school. The best situation is if no-one gets shot, neither the intruder nor the intended victim. That can only be ensured if neither party has a gun. The moderately bad situation is if shots are fired. Someone--the intruder, the intended victim, or possibly both--may die. The worst situation is if the intruder has weapons and the intended victims do not. In that case, as in Sandy Hook School, many people may die.

We can put these outcomes into a table, similar to the one for the Prisoner's Dilemma.

Intruder is unarmed (cooperates) Intruder is armed (defects)
Victim is unarmed (cooperates) Neither gets shot (best result) Many victims could be shot (worst result)
Victim is armed (defects) Someone gets shot (moderate result) Someone gets shot (moderate result)

The difference between the two sides of the gun debate, therefore, may lie in a difference of viewpoint about whether the death of a criminal is desirable or the death of a victim defending himself is acceptable, or both. From one point of view, to have criminals shooting each other is even a net benefit to society. The alternative view is that a death is a death, and we should find ways to avoid it.

A TED talk by Jonathan Haidt spoke about the differences in values between conservatives and liberals. I think it might explain the different opinions above.

The applicability of his talk to gun control is that a "liberal" set of values includes "do no harm" and "fairness," but a "conservative" one includes both of these as well as three others. The relative importance of the five basic values for different people can be graphed as in this screenshot from Haidt's talk.

The data for this graph come from American citizens. It shows that conservatives value group membership and respect for authority about as much as they value being fair or doing no harm. Since a criminal is self-defined as being outside the group, disrespects the victim, and defies authority, the voice in a conservative's mind that says "do no harm" competes with other voices that say "punish, hurt, kill."

Even people who value every life may not believe that a gun-free environment is achievable. If it is not, they think, then it is better to try to limit the number of victims by arming more potential victims.

Are they right? Is a gun-free zone impossible? The experience of the world is that it is possible. For example, Japan is virtually gun-free, and has almost no deaths by shooting.

Despite the experience of such countries, many opponents of gun regulation state explicitly that laws might limit the ownership of guns, but the defining characteristic of a criminal is that they break laws. They say that criminals will always have guns.

In the American context, they have a point. "No-one has guns" is not an option there, thanks to the Second Amendment of the American Constitution and a 2008 Supreme Court Ruling. The Second Amendment reads, "A well regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed." The Supreme Court ruling in District of Columbia v. Heller clarified that this amendment did not merely apply to arms borne by such "well-regulated militias" as the National Guard, but whoever (subject to reasonable regulation) wishes to keep and use arms for lawful purposes, such as self-defence.

The gun control laws in Canada, where I live are, at the very least, more consistent than the hodgepodge of different laws in the United States. A few towns there have even tried to make a point by mandating gun ownership. (For example, Kennesaw, Georgia). The lack of consistency in gun laws and their enforcement in the United States must contribute something to the high number of shooting deaths there.

I would love to see the United States reduce its rate of deadly violence to a similar level, or a lower one, than other developed countries. However, unlike in Canada, the culture in the United States simply does not allow effective gun control. The people's attitudes not merely to guns but to governments and law enforcement oppose it. My only hope for that is the gradual aging of the population due to a low birth rate. I believe that, if a person has reached the age of eighty without shooting anyone, then the chances of him beginning are low.


Update (14 March): The musings above focus on different values among advocates and opponents of gun control. I wonder now if the matter might, more simply, be a matter of trust. In the Prisoner's Dilemma, the prisoners might not testify against each other if they each trust the other not to testify. A reason to trust might be experience with the other's behaviour that was built up over a series of interactions. (The book The Evolution of Cooperation by Robert Axelrod is a fascinating discussion that includes this point).

Perhaps gun control advocates simply trust in the goodness of their fellow man and the efficacy of law more than gun advocates do. That trust would make the optimum solution--no-one has a gun--seem achievable. To a gun advocate, it would simply run against human nature, so the second-best option--the victim has a gun--would be the best that can be achieved.


Update (14 March): I didn't explain what I meant by attitudes to guns, governments and law enforcement, though the article I linked to does. Here is a sample I stumbled on: a science fiction author (of all things) named L. Neil Smith. This is from his home page:
Over the past 30 years, I've been paid to write almost two million words, every one of which, sooner or later, came back to the issue of guns and gun-ownership. Naturally, I've thought about the issue a lot, and it has always determined the way I vote.

People accuse me of being a single-issue writer, a single- issue thinker, and a single- issue voter, but it isn't true. What I've chosen, in a world where there's never enough time and energy, is to focus on the one political issue which most clearly and unmistakably demonstrates what any politician—or political philosophy—is made of, right down to the creamy liquid center.

Make no mistake: all politicians—even those ostensibly on the side of guns and gun ownership—hate the issue and anyone, like me, who insists on bringing it up. They hate it because it's an X-ray machine. It's a Vulcan mind-meld. It's the ultimate test to which any politician—or political philosophy—can be put.

If a politician isn't perfectly comfortable with the idea of his average constituent, any man, woman, or responsible child, walking into a hardware store and paying cash—for any rifle, shotgun, handgun, machinegun, anything—without producing ID or signing one scrap of paper, he isn't your friend no matter what he tells you. 
This is closer to a non-negotiable article of faith, from my perspective, than a subject for reasoned discussion and compromise. Surprisingly, the author spent some of his youth in Newfoundland, the only North American jurisdiction in which police officers did not carry sidearms, though this changed in 1998.


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  2. I've thought about gun control as game theory as well, and in the exact same table you created, but my labels were different than yours. I think you've labelled the outcome results as a broader "all life is sacred" kind of approach, whereas I've thought about with karma and more of a 'John Rawls Theory of Justice' kind of approach. For me, the ideal outcome is Victim is armed, Intruder is apprehended and/or shot if violent, particularly if I'm the victim. Speaking on behalf of victims, I would still prefer to be armed myself and the intruder not, and would consider that the ideal position, if an intruder insists on intruding. But I think being armed increases the confidence of an intruder to intrude in the first place - you know you are armed, but your victim is not necessarily, so your odds of winning are good. With so many guns being abundant in the USA, potential victims know that intruders are more likely to be armed than might be the case in Japan, or the UK, etc. In game theory, every participant takes on the action that leaves themselves in the best position in anticipation that the other party will do the same. The nash equilibrium, then, is for both parties to be armed. That said, by destroying and banishing all guns among civilians, the need to be armed yourself is diminished significantly because the probability of facing an armed intruder becomes dramatically reduced. Unfortunately, there are more guns in the united states circulating the population than there are people. I guess it will have to be a shooting gallery to the bitter end. All that said, I'm Canadian so it's only minimally my problem or my business, but I'll be curious to see how much carnage takes place in your country over the years. I say it's minimally my problem because we do share a border, and guns are likely to make their way across, which is not something that makes me happy, but what can I do.

    1. Hello, Matt

      First, thanks for your comment. I appreciate getting other points of view.

      First, you distinguish your approach based on "karma" from mine in which "every life is sacred." I suppose I don't want to write off the lives of either side in an altercation because I am no lord of karma, with the ability to judge men's souls. From my lowly status as a human being with limited insight into my fellow men, I'd say that it is often hard to decide who is on the side of the angels.

      I'll take as an example the Trayvon Martin case. In that, Trayvon Martin was walking around a neighbourhood without breaking any laws we know of; George Zimmerman was patrolling the neighbourhood looking for suspicious characters; each thought of the other as an anomaly and a threat; Trayvon ran; Zimmerman followed; an altercation arose; Zimmerman, "in fear for his life," shot the 17-year-old boy. The courts found that Zimmerman was the guy on the defensive here and that his claim of shooting in self-defence was credible. On the other hand, though, Zimmerman chased someone down and confronted him, which makes him the aggressor. Clearly, it would have been better if neither of the two had been shot, as neither deserved to die that night.

      Interestingly, I have recently watched the British tv series "Luther" with my son. He was shocked (shocked!) that the British police did not routinely carry weapons. The carrying of weapons can become an expectation, a social default, if we're not careful to promote the opposite.

      Thank you for the reference to John Rawls. I hadn't heard of him before.


  3. By the way, this link is on-topic and may make you smile: "Guns, Guns, Guns" by the Guess Who:


  4. I enjoyed your article. Reading about the increase in gun sales following the San Bernardino massacre reminded me of the Prisoner's dilemma. I entered those search terms and found you had already thought this one out after Sandy Hook.

    Two people go to work. The options are:

    #1 Neither is armed so no one will be injured/killed.

    #2 One person is armed and so the other person *can* be injured/killed

    This is where it gets messy -

    #3 BOTH of them are armed meaning there is the chance that a)
    both get injured/killed; b) Person A may be able to defend against an attack by Person B (and vice versa); c) no one dare attack the other (the "armed society is a polite society" idea).

    The best outcome for everyone is option #1 (no worries; no injury/death). But with eroded trust people are going for #3.

    1. I'm glad that other people are thinking along the same lines as I do. I think a problem is that people often think of guns (which are by nature OFFENSIVE WEAPONS) as DEFENSIVE WEAPONS.

      The only way that having a gun could be an actual defence against an armed opponent is if it created a Mexican stand-off, a situation in which neither party dared to shoot because he might then be shot.

      The imagined situation resembles the nuclear standoff between the Soviet Union the United States during the Cold War, codified as the Mutually Assured Destruction (MAD) doctrine. However, there are two small differences between the Mexican Standoff and MAD. In the former, destruction is not "assured." That is, I might shoot too late, or I might miss. Also, the destruction might not be "mutual." The first one to shoot may be unscathed, if the shot is a good one. Therefore, the other party has an incentive to shoot me before I can shoot him. That doesn't sound like a great defence to me. I'd be better off with a REAL defence, such as a combination of a bullet-proof jacket and a pair of good running shoes.

      If I did have a gun, I'd be safer if I took a hostage than if I tried to face down the attacker. In many cases, the attacker would not dare to shoot me because of the chance that I'd kill his loved one. However, I'd have both moral and practical problems implementing that one in an emergency.

      So, let's be clear. Rather than providing a defence, a gun provides a chance to initiate the violence. The gun could increase my chances of survival only if I shot first, with accurate aim. That means that I would be the first person to initiate deadly force, in a situation that may not have called for it.

      A case from the States illustrates pretty well the reasons for my unease about this way of justifying the first use of weapons.

      A man chased a burglar from his home and down an alley. As the burglar was fleeing (i.e. not attacking), she shouted that she was pregnant. The man then shot her twice in the back, killing her. The article did not specify that the intruders were unarmed, but the fact that they ran when the homeowner took up a gun is an indication that they had no firearms.

      When I read the story, the police were considering charging the dead woman's accomplice with murder because he "is accused of participating in a felony that led to a death." The man who did the killing was not charged. (Search Tom Greer and Andrea Miller for details).

      The unarmed, fleeing, and possibly pregnant woman was a criminal. She did wrong. She was guilty of breaking and entering, of assault and battery, and of an attempt at theft. However, not one of these is a capital crime, as far as I know, and so not one justifies her killing, despite the provisions of California law.

      So, I guess I'm saying that option #2 (one person is armed) can be as morally messy as option #3 (both people are armed).

      I suppose that my bottom line is the definition of a state that the philosopher Weber came up with: it is the entity that has a monopoly on legal violence. That's not a definition that the majority of Americans (to judge by the laws and court decisions) can accept.

      What do you think?

      -Gareth Jones

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  6. There’s a lot of fulmination about the 2nd amendment and losing rights, and defenders are trying the “it’s too late anyway, there are > 300 million guns in the US” argument. There’s a simple way to get around both – if you can’t make it difficult for the wrong people to get guns, make it difficult for them to get ammunition.
    History of the 2nd Amendment