Firearms, Euvoluntarity, Game Theory and Complexity.

Friend of EE and all-around great guy Art Carden poses the following question on Facebook:

In light of the CT shootings, people are talking about a lot of things: gun control, mental illness, culture, etc. I have a network full of people who deal in ideas and evidence for a living, and I'm interested in their feedback. In the interests of advancing evidence-based discussion, please answer the following:

1. Do you think the government should do more to restrict access to guns?

2. On the basis of what arguments or evidence?

3. What arguments or evidence would make you change your mind?

Ground rules: no insults, name-calling, or ad hominem attacks. Seriously. I might publish this as my December Forbes contribution, and you'll be welcome to sling mud over there if that's what you're in to.

Please answer all three questions. [edited for some minor typos]

This is an empirical question and I find Lott's work on guns and crime convincing. I also believe that there's more to the story than even the most carefully-controlled econometric provides. The reason I believe this (which points to answering questions 2 and 3) can be found in Ayres and Donohue's "Shooting Down the More Guns, Less Crime Hypothesis" (2003). They find quite a bit of sensitivity with regard to specification, which is consistent with my own crime regressions. Unfortunately for the curious researcher, even the best-specified microeconometric investigation cannot get at mens rea. Without some theory, trying to peer into the minds of criminals is futile. Gun control is one possible policy response to horrible tragedies like school shootings, but it's not the only one, nor is it necessarily the cheapest or most effective.

So what is the theory? I have a hunch that this is where opinions most differ. I suspect that gun control is one of those issues that goes beyond simple moral intuition. Regular folks, median voters if you will, wrestle with the language of the US Constitution when pondering their priors and this forces them to think logically about their stance. The median voter may not always think clearly or carefully, but there is thought there. I can't say for sure what the specific thinking is in the minds of the electorate, but I can share how I'd approach the question. To do so, I need to give a poor man's primer on game theory. If you're already familiar with the subject, or if you're bored by this sort of thing, please skip down a few paragraphs. I am emphatically not EE's resident game theory expert. JR has more practice than me (and is in general a much smarter dude), and the GTM has been publishing peer-reviewed articles steeped in game theory since I was in short pants. This is merely a quick overview, intended more to illustrate just how difficult this question can be.

The chief elements of a game are: players, actions, payoffs, and strategies. Most textbook examples use two players, but when dealing with policy questions, abstracting from reality is more costly. Do we consider extant majority-age American citizens to be players in the Game of Guns? How about foreign nationals? Do future discounted American citizens deserve a seat at the gaming table? How should we account for the wishes of past generations? Please note that I'm not being facetious here. Many of the appeals made are either "for the children" or for the more nebulous "unborn generations". Identifying relevant parties is no simple matter. Actions are similarly complex. Carden framed his question around access to sidearms (I'm a Navy veteran, and aboard ships, a "gun" isn't something a person can pick up and fire. Guns are mounted weapons and are fired from a console), but what if an action might be something like "institute 48-hour media blackout?" What if an action could be to refit public spaces with armored doors and panic buttons? Outside of blackboard beard-scratching, the set of possible actions is limited by the extent of human creativity. Payoffs, likewise, tend to be stochastic in the real world. I might harumph past the distinction between payoffs and expected payoffs when I'm explaining game theory to a 19 year old undergrad, but turning theory into practice, I cannot ethically dodge questions of systematic bias on the part of any player, including the policy-maker. Both the probabilities and the ordinal payoff amount is subject to mis-estimation. This all adds up to the actual strategies employed (being that the strategy is a function of the other elements of the game) can be shrouded in uncertainty if not downright non-ergodicity. Understanding and appreciating the depth of imperfect information in society helps us to forecast unintended, unforeseen and unforeseeable consequences.

The four non-trivial types of strategic games are: a) Prisoner's Dilemma, b) Battle of the Sexes, c) Hawk-Dove and d) Coordination Game. Each of these games have different solutions and different implications for intervention. Gun ownership as an infinitely-repeated PD reacts differently to third-party intervention than a H-D game. Apart from misrepresenting the elements of the game, folks may be assuming a society is playing a game that does not accurately mirror reality. Civilian gun ownership may be a coordination game in a universally disarmed society (or in a meta-game sense), but a Hawk-Dove game elsewhere.

Game theory allows the theorist to predict the behavior of rational players based on the architecture of the game and on a few assumptions about the rationality of the players. Much of the fun of experimental economics rests in finding laboratory results that run contrary to the predictions of the sketchpad theory. Apparent violations of Arrow-Debreu rationality add another layer of strategic uncertainty to an already complex game. To reach a conclusion that the government should restrict access to guns, an analyst would have to be able to show that this intervention is a K-H improvement over the status quo and over reasonable alternative interventions. I think there's good reason to be a priori skeptical of this, and it's mostly because I think the assumptions needed to generate this conclusion are contraindicated. For gun control to work as advertised, the state would have to identify and disarm future violent criminals. Because of knowledge constraints, practical policy often ends up being municipal handgun bans or assault rifle bans. This sort of policy assumes a coordination game: fiat legislation crosses out the (Gun, Gun) node, so the equilibrium is now (Unarmed, Unarmed). It seems more reasonable that the actual game is Hawk-Dove and the equilibrium is (Gun, Unarmed), acknowledging that people who get a large payoff from a horrible mass-murder atrocity will be willing to pay substantially for horrific infamy. The same reasoning applies to common violent crime. If criminals assume citizens are unarmed, they will be more likely to commit armed robberies. Naturally, there are more reasons than just the existence of legislation to form beliefs over whether or not someone is armed, but we're looking at policy here, not practice.

So what are some ways to limit the damage caused by deranged maniacs on shooting sprees? What sort of policies are directionally euvoluntary? What is the appropriate scale for precautions? Well, if the game selection is wrong, gun bans may increase the risk of violent incidents and could result in deadlier outcomes. Not to be flippant, but if I can't defend myself using lethal force in a horrible scenario, I'd call that a case of ex post regret. But that's what I wouldn't do: I wouldn't try to ban guns. I think another thing I wouldn't try to do is to assume a policy scale. For example, suppose a good way to defend against a spree shooter is to build emergency exits to the exterior in each room combined with airbag-style barriers built into door frames, activated by a wall switch. It seems obvious to even a casual observer that the risk-adjusted cost effectiveness of this sort of intervention will depend heavily on local conditions. All costs are opportunity costs, and policy makers under the Capitol dome lack the requisite local knowledge to solve that problem.

The game is what it is. Wishful thinking and good intentions are insufficient to change a H-D game into a coordination game. It might be possible to alter some of the payoffs though. If killers' objective function is to maximize post mort infamy, the FCC might consider drafting rules under the obscenity clause to fine publishers that sensationalize spree killing events. Or NCLB guidelines could be modified for mental health screenings. I'm sure you can think of your own interventions, and perhaps it's worth considering some (and not others, including but not limited to the two I just shared). The point is, it's not immediately clear that one particular policy will best provide a socially optimal outcome, nor that that one particular policy will pass a reasonable cost-benefit analysis for a large constituency. Spree killings have no easy solution, political kayfabe notwithstanding.

Answering the Dub-MOE's third question seems tough. I'm familiar enough with the econometrics first-hand to be skeptical of empirical claims. I'm also leery enough of the knowledge problem to shy away from policies aimed at national-scale solutions. To change my mind, I suppose someone would have to convince me that their game theoretic model is the correct one, then bolster that theoretical model with better empirics than currently exist and be able to properly account for hidden costs and unintended consequences.

Firearm ownership by responsible citizens is super-euvoluntary: arms are a last bulwark against tyranny and the regret experienced by failure to responsibly own and operate a sidearm may outweigh the regret from ownership. Conversely, firearm ownership by criminals and the irresponsible is sub-euvoluntary. Effective policy must consider the benefits of the former and the costs of the latter.

[edit] Many thanks to Professor Carden for reviewing my copy.