Game Theory Applied to Gun Control

[Sebastian the Ibis]

I am going to be having drinks with a very academic economist/lawyer next week and I know Heller and gun control will come up. I am planning to argue against gun control in terms of game theory, and I would like to know if anyone sees an error in this:

Assumption 1: Anti-gun laws impair law abiding firearm owners more significantly than criminals since criminals do not follow the law.

Assumption 2: In a confrontation the best to worst situations would be:

1. Good guy armed, bad guy unarmed.
2. Good guy unarmed, bad guy unarmed.
3. Good guy armed, bad guy armed.
4. Good guy unarmed, bad guy armed.
(arguably 2-3 switch, however I am thinking in terms of the average American not the average highroader.)

If the above assumptions are accepted, restricting guns is counterproductive. Any reduction in armed bad guys will lag far behind the reduction of armed good guys since laws affect those that obey laws more directly than those that do not. Thereby with anti-gun laws situation 1’s become 2’s, and 3’s become 4’s.

This argument assumes that guns can be used to harm people either good or bad, which is usually an Anti’s hole card. However, admitting that guns can be used to harm people; shouldn’t you, as a good guy, should be armed so that situation 2’s become 1’s and 4’s become 3’s?

Does anyone see holes in the above reasoning?

If anyone does not think it is a good idea to admit that guns can be used to kill people can you please say why?

Thanks

 

[Eric F]

Does anyone see holes in the above reasoning?

YEah look here

I am planning to argue against gun control in terms of game theory

thats fine if you do it before....

I am going to be having drinks

but everything looks good so far

 

[jobu07]

This is a novel approach to take. I can see it use in trying to "get through" to some of the more educated folks out there. Sort of putting it into their terms. Let us know how it goes.

 

[jakemccoy]

The logic is a bit rigid but fairly sound. Whether or not it will work is another issue altogether.

You should probably avoid quick counter arguments in your conversation. I've found that people general shutdown if you treat the discussion like beach volleyball.

Avoiding quick counter arguments is hard because you've probably heard all the anti-gun arguments and instantly know the answers. It doesn't matter. When the hairs on the back of your neck start to stand up, and they will, take a deep breath first. Maybe tell a joke or something to ease the tension.

Pretend you're a well-respected professor leading a classroom discussion. They always keep their cool, and the information always sinks into the smart students' heads.

 

[Loomis]

I like it. But I seriously think you are WAY understating your argument. There's no reason to go to your fight wearing kid gloves, is there?

Firstly: firearms are called the great equalizer. This is because when everyone has guns, the biggest, meanest, bad guy is approximately on even footing with a small weak good guy. Therefore, I object to your ranking and strongly argue for you to switch number 2 with number 3. In the event that a bad guy is physically weak and the good guy is physically strong, then your ranking would be accurate, but only then.

Secondly, you are leaving out the deterence factor. Since the bulk of the crime committed is committed by a very small minority of the general population, we have a situation of repeat offenders. If more citizens are armed and willing to fight back, those repeat offenders are not going to be able to continue a crime spree very long. Sooner or later they will get stopped by one of their intended victims.

Do you get the significance of that?? It means that each time a good guy wins a battle with a bad guy, HE DOES NOT PREVENT A CRIME, HE PREVENTS ALL CRIMES YET TO BE COMMITTED BY THE DEFEATED BAD GUY.

So take that to your anti-gun/pro-gun argument and tell the wuss that every time he chooses to be a dam pacifist, he is contributing to the victimhood of a multitude of future victims.

 

[Old Fuff]

I think your opponent will argue that it's true that criminals don't obey laws, but strict control - or better yet an outright ban, would deny them a necessary source of supply.

If so, you have the choice of pointing out that prohibition hasn't slowed the availability or use of controlled substances, and instead given the criminal community another source of wealth.

Then there is the grand experiment in the United Kingdom...

 

[BruceRDucer]

/

3. Good guy armed, bad guy armed.
Sebastian the Ibis

I'm no rocket surgeon, but the "ARMED" specification is rather Black & White, allowing for no degrees of being armed.

You know, like as in a guy having a pipe, chain, or driving at you in a forklift, etc...

In a game, expect the unexpected, and watch out for those Knights and Bishops!

/

 

[Zedo]

Yeah, bad idea --

It's not a "game." It's a Constitutional Civil Liberty. It's not about logic and probability, it's about the law of the land. It's not the Bill of Games; it's the Bill of Rights.

 

[jakemccoy]

Then there is the grand experiment in the United Kingdom...

Along those same lines, Mexico is a closer analogy to what would happen if major cities like LA and Miami instituted complete gun bans. We're already not too far away.

 

[JackBurtonJr]

Does anyone see holes in the above reasoning?

Watch for a couple of things...

Always make sure you and he are defining your terms in such a way that you are both using the same meaning.

Let me give you an exaggerated example... you say "criminal" which means a social deviant who should be stopped by whatever legtimate means are available... your friend says "criminal" and he means a socially misguided youth who is merely trying to even the obviouisly unequal playing field of America that he had the misfortune to be born in.

This means that the natural assumption on your part is that shooting him is a good thing, and the assumption on his part that shooting him is just one more tragic example of how those we oh-so-quickly label societal outcasts just cannot catch a fair break.

So when you both discuss the idea of a citizen carrying a gun to "shoot" the criminals, how can you possible agree on if it is a good or bad idea, regardless of how well you present your argument?

This problem can plague almost any discussion of this kind, and is, I think, the main reason we wind up so often talking past one another.

Also, economists tend to think in quantitative terms. If you start in using numbers they can usually eat the other side alive. If you're not using something absolutely rock solid as a number... leave it out.

If anyone does not think it is a good idea to admit that guns can be used to kill people can you please say why?

I'm not sure that even needs to be part of the discussion since neither the good guy nor the bad guy needs to "kill" the other person to force them into compliance. It's an unnecessary complication to the discussion.

Might want to look and study the free book Gun Facts before the meeting.

 

[jakemccoy]

I'll add that there is a real life example to counter every anti-gun argument out there. There's nothing new under the sun. You have to know your facts and history though.

 

[MutinousDoug]

Loomis brings up a good point that the game may be played differently if it is played only once or played iteratively: The more times the bad guy wins; the worse it is for all the good guys. The converse is also true.

 

[Jorg Nysgerrig]

It sure sounds like you are trying to do a PD game and in that case, I don't think you've properly set up your outcomes for a traditional Prisoner's Dilemma game. Because of that, there are several holes. Unfortunately, I'm out of time and unable to elaborate. You have an interesting premise, but it needs a bit of tweaking.

 

[ctdonath]

The fundamental problem with gun control, which somehow needs reflecting in your game-theory system, is that the interests of the individual may radically differ from the interests of the group. I usually put it "statistics mean nothing when they happen to YOU." Those who are not directly affected by an incident care far less about how the incident is handled than the people immediately involved - to wit: strangers are expendable, I'm not.

 

[tigre]

I'm no rocket surgeon, but the "ARMED" specification is rather Black & White, allowing for no degrees of being armed.

You know, like as in a guy having a pipe, chain, or driving at you in a forklift, etc...

Or, just a plain ol' "unarmed" bad guy against a much smaller or otherwise physically outmatched good guy/girl.

 

[Durruti]

Both the good guy and the bad guy have to choose whether to be armed. The good guy faces two situations: either the bad guy is armed or unarmed. If the bad guy is armed, the good guy is better off armed, since outcome three is better than outcome four. If the bad guy is unarmed, the good guy is still better off armed, since outcome one is better than out come two. Thus, armed dominates unarmed for the good guy.

A similar logic applies to the bad guy, who would also prefer to be armed, regardless of whether the good guy is armed or unarmed. Since armed is the dominant strategy for both the good guy and the bad guy, there is a Nash equilibrium at outcome number three.

Therefore, both the good guy and the bad guy go armed and wind up in outcome three, even though both would be better off in outcome two, where both are unarmed. This is similar to the Prisoner's Dilemma, where both players cheat, even though both would be better off if they cooperated.

Now, your friend could turn the logic around and say that this means that government should have a role to play in eliminating guns from society, since that improves people's lives by moving folks from outcome three to outcome two. This, of course, ignores the fact that bad guys are more likely to get guns in such a situation than good guys.

Kind of interesting. I like MutinousDoug's point, too. If such a situation is played out iteratively, instead of as a one-off thing, I wonder what you might see. It could be similar to the Prisoner's Dilemma, where initial cooperation followed by a tit-for-tat strategy is the best.

Of course, I don't know how many of us want to start off assuming goodwill on the part of the bad guy So maybe we're doomed to an armed society

 

[Gentleman Ranker]

Another problem that you may encounter is that, while game theory can be quite useful in analyzing the logic of certain situations (and can even go n-person or across time), game theory itself provides no basis whatever for assigning the payoffs to the game. All your colleague has to do to destroy your argument is attack your payoff assignment.

BTW, I don't see any assignment of payoffs to the players in the quasi-matrix you've constructed.

If you want to take that kind of approach, I'd start with John Lott's work. It's not explicitly game-theoretical, but it's based on "economic" decision-making and has some foundation in empirical research.

regards,

GR

 

[Sebastian the Ibis]

Durruti:

I agree that there is a NA at 3 if that were the only selection. However, I guess what I should have fleshed out a little more is that this is a dynamic system, since the other choice is more gun restrictions or not. The selector in this situation is a voter, who would self identify as Good Guy. (I am assuming that criminals don’t vote for gun laws to make their professional lives easier.)

Therefore assuming that more gun laws reduce the number of armed good guys faster than the number of armed bad guys, why do some voters continuously select that option? Which yields more 4’s and 2s?

I suppose they are hoping that with enough laws all guns will eventually be eliminated, but that is the same logic that says that infinitely taking away half of what is left, from half is what of left, from half of what it is left will eventually yield zero.

 

[Sebastian the Ibis]

However, Ctdonath raises a good point.

To analyze the societal question create a new person – Bystander.
And change the designation Good Guy to Victim (for the sake of clarity)

Then assume that Voter can randomly be assigned the role of Bystander or Victim.

If voter is a Victim he will benefit the same as Good Guy- always better to be armed and for Bad guy to be unarmed.

However, if voter is a Bystander 1 or 2 could be the better situation.

If the game is not replayed then 2 is best situation since if neither is armed, there is no possibility of Bystander catching a stray round and bystander does not lose anything since they can run.

If the game is replayed as MutinousDog and Loomis allude to then 1 is probably the best choice since the Bad Guy is stopped and the game is not replayed with the possibility that Bystander becomes the Victim in the next game.

This, really makes a lot of sense since Gun owners/carriers who assume and prepare for bad situations every time they carry, would probably assume a repeating game where the game would replay until stopped. Whereas, sheeple who never thought it could happen to them in the first place probably assume a single game.

 

[jonmerritt]

I have always found that when the anti-gun person runs into the BG with a gun, and is getting robbed, beaten, and treated like a typical unarmed victim, there stance on guns, for some unknown reason, tends to lean rather dramaticly twords pro-gun. As to why? We will never know. Some of them also have been known to scream even louder anti-gun, while keeping there own guns. Aren't politics wonderful?

 

[Zundfolge]

I have always found that when the anti-gun person runs into the BG with a gun, and is getting robbed, beaten, and treated like a typical unarmed victim, there stance on guns, for some unknown reason, tends to lean rather dramaticly twords pro-gun.

Not always. Some of the time it simply hardens the anti-gun person's resolve and makes them twice as anti-gun (the logic being if there were no guns they wouldn't have been victimized). Jim Brady is a good example (although I don't know if he was an anti before being shot).

Same thing with bringing it up in an argument.

Keep in mind that a sizable percentage of anti-gun folk practice Magical Thinking and honestly believe that banning guns = no more crime with guns and will refuse to acknowledge the reality that bans have not and can not work.

 

[RNB65]

Whoa... This is deep.

Someone call Princeton and see if John Nash can help us out.

 

[ErikS]

I see a problem in the assumptions.
You are basically setting up the assumptions based on a randon good guy and a random bad guy, put them together, and look at possible outcomes.

However, any confrontation is initiated by the bad guy. The bad guy wont ever start a confrontation if he suspect he might be in a 1 or scenario, nor a 2, unless he has a huge advantage in size. So in real life, the number of confrontations will be heavily scewed to 4, and 2 in the cases where the bad guy have a big advantage in size.

If you want to argue game theory, wouldn't it be better to argue it from te bad guys view, like a "prisoners dilemma". If you were a bad guy, which scenario would you pick? You could change if you are armed or not, but you cant change if the good guy is armed. So you will try to make sure you have the advantage, by trying to avoid armed targets.

Now, assuming total gun control, noone can own a gun. (and for the sake of argument, that includes all bad guys here) You know you are in a 2 scenario, so what will you do? Hang outside a gym and try to rob the 300lbs guy with no neck coming out? No, you will try to pick the small guys, women, and elderly people, thereby putting you in a distinct advantage.
Now assuming those people could be armed, how will that change your choices? First thing it will do is complicate it. You will no longer have safe targets, that you know you can just confront at will.

So with gun control, bad guys can choose their victims and have a close to 100% success rate, just based on picking targets that look small and weak.
When people can own guns, the bad guy find himself in a game theory choice situation, where he wont know if the other person is armed or not. This will make it harder for him to make a choice, and even then he will guess wrong in a lot of cases, lowering his successrate to about the opposite percentage of the percentage of people carrying. (Give or take)

Now, as a bad guy, you want to increase your success rate, so what would you do? You would try to find targets that you were fairly sure weren't armed. You would not try to rob a cop bar, or a gun club, but a gun free zone would be a good place to start. Or a house that has a pro-gun control sign outside.

Trying to argue game theory based on a one on one scenario is wrong, it will never be an equal match if the bad guy can help it, he will always pick the weaker target. (i.e. a target he thinks he can beat)
That's why gun control is morally wrong, it denies people that are elderly, physically weak, or outnumbered, the possibility to defend themselfes succesfully.

 

[LightningJoe]

Even if you make him understand, he won't like it. You can't make the horse actually drink the water.


Once, I was talking to my boss's boss (a northerner who didn't like Texas) about gun control and I brought up the example of Kennesaw GA. I forced him to grasp that the criminal does not want to break into houses in a town where everybody has a gun. I saw in his face that he actually understood (apparently for the first time in his life). And he didn't like it. So, he sat there speechless for about 20 seconds while he processed the new information. Then, he said, "Thus making crime artificially high elsewhere!"

 

[tigre]

Great post, ErikS. And a very good argument for people who think everything would be great if nobody had guns at all. Even if that were possible, some people don't need guns or any other kind of weapon. I saw a guy last night whose arms were as big as my legs. A hypothetical world where there are no weapons just puts people like that at an advantage. It frustrates me to no end that so many women support gun control, because that's the kind of world they seem to want, where just being bigger than your intended victim is all that's needed.