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.

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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.

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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.