Sunday, October 22, 2006

The Efficiency of Innocence

When economists talk about efficiency we are usually talking about the costs and benefits for all society. Benefits minus costs are the "social totals" and the most efficient items are those that maximize these totals. Doing this type of analysis can be difficult because one must include all costs and benefits for everyone. It's usually impossible to get an exact figure so an estimation works pretty well. Still, it can be a daunting task.

I've decided that the "innocent until proven guilty" reasoning in US legal courts is efficient so, briefly, I'm going to demonstrate my logic. (If you don't want to go through all the assumptions and logic, skip to the conclusion at the end of the post.) Assume a crime, such as rape or murder, and a trial of an accused, the police's chief suspect. Assume that the police stop investigating the crime when the court finds a guilty party and the police keep investigating otherwise--not completely true but true enough for our analysis. Assume all third parties are treated equal--one family's feelings aren't inherently more valuable than anothers'--and the pain of seeing a family member go to jail is roughly equal to the pain of having a crime against a family member go unsolved. Assume the court is wrong by an even-handed chance (see below).

We have four scenarios to consider based on if the accused is actually innocent or guilty and what the courts find him as:
-declared Innocent if actually Innocent (IiI)
-declared Innocent if actually Guilty (IiG)
-declared Guilty if actually Guilty (GiG)
-declared Guilty if actually Innocent (GiI)

The first two represent the current legal system which favors claiming someone is innocent. The second pair represent an alternative system: "guilty until proven innocent" where guilty is the more likely verdict. Because these will chiefly determine what kind of error is most popular in a given legal system, this divide is how we will make our analysis.

IiI and GiG cancel each other out. In both cases the system did exactly what was most efficient to do. Social totals were maximized. It's the errors that are interesting.

Most of IiG and GiI cancel. The victim's family will suffer and the accused family will celebrate for IiG and the reverse is true for GiI. Similarly, effort needed for the case is on the state for IiG because they have the burden of proof; that effort transfers to the defense in GiI so once again we see a canceling out. The moral pain of sending a good man to prison is roughly balanced by an equal level of pain of letting a killer free. In both cases, the crime can be repeated as the bad guy still roams.

This is where we see the difference. In IiG, the crime is unsolved. Not only are people more alert because that crime could be repeated but police are still investigating the crime. The liklihood of correcting the error is much higher than in GiI where the crime could occur again but people's guards are down and the police aren't on alert. (In fact, in GiI it's more likely the bad guy will get away because everyone will be caught off guard.) Because everything else is a wash, this edge--which is by no means minor--demonstrates "innocent until proven guilty" better serves society.

For those that didn't read the whole post it is better for the law to assume people are innocent because the bad guy getting away is easier to correct than the good guy going to jail. In the former, society knows there's a problem still out there and thus makes it cheaper to correct. In the latter, the problem can occur with greater liklihood (or much longer) without it being stopped. We can see this in immigration policy: society never misses the good people rejected from the US so that drop in social totals would persist for a long time but accepting the bad guys allows us to kick them out when they prove themselves as the bad guys. Alex Tabarrok and Dan Klein make a similar arguement about the FDA: if a bad drug gets passed, society knows it and can remove it before too many people die. If a good drug is rejected, people can be dying for years and no steps taken to correct the problem.

This is ultimately the old distinction between the seen and the unseen. People focus on what they can witness first hand. They tend to ignore the unseen costs because the never were even aware of them. Sending the innocent to jail, rejecting a promising citizen and never benefiting from a great drug are treated as non-losses to society and so they are rarely corrected for even if they are just as damaging as their obvious counterpart.


SmoothB said...

The moral pain of sending a good man to prison is roughly balanced by an equal level of pain of letting a killer free.

Not to sound crazy or anything, but isn't the general defense of "innocent until proven guilty" that the above is quite clearly not true?

I'm just wondering because I'm not sure if your logic works. If the FDA okays a drug that's actually poisonous, they could later ban it. But if the court lets someone go free who is actually guilty, that's it. You can't ever put that person in jail for that crime because doing so constitutes double jeopardy and is against the constitution.

David said...

I claim the two as equal balance of immorality because both are unjust results from an ethical standpoint. I get a gut reaction that it's worse if the innocent goes to jail than if a murderer is set free yet I can't explain why so I assumed them to be equal. I would like to know why you think it is so clear.

Your double jeopardy point is well taken as people cannot undo a bad case (I personally think there's room for exceptions in the case of new evidence but oh well). However my analysis allows for police to pin the bad guy on other things and I place emphasis that if let go, the bad guy could strike again, in which case he would be tried again (not for the same crime, of course, but still tried). The key idea is in GiI, the police stop trying and there's little chance for correction. In IiG, that chance is much larger, even with double jeopardy.

SmoothB said...

I'm mainly saying that since we do feel that way and since we do give precisely that reason in defense of a long-standing rule in common law, there's a fairly good chance that our judgment is correct even before we put our moral judgment into words.

But how’s this: if a crime is committed and you let a guilty person go free, another bad thing may happen (we assume that someone who commits one crime is more likely than average to commit another) but if you imprison the innocent, then you know another bad thing will happen, since you have in fact imprisoned the innocent (and so committed a crime yourself). This may go to our general sense that sins of commission are worse than sins of omission – allowing something bad to happen isn’t quite so bad as actually doing the bad thing. It may also go to a need for basic norms that encourage trust (i.e., presume innocence) and civil society. Then there’s the basic need to restrain the state: guilty until proven innocent gives the government the de facto power to imprison at will. Finally, this might be a recognition of rather low crime rates – if crime is low, increasing it slightly by presuming innocent is not really such a big deal, whereas we might reconsider the matter if crime was very high (witness how, in the wake of 9/11, we have in fact begun revising our civil liberties).

David said...

Admittedly your arguements support my case that innocent until proven guilty is more efficient but I still find myself disagreeing with your logic, at least in part.

You say: "....if a crime is committed and you let a guilty person go free, another bad thing may happen...." You don't thinking letting the bad guy go free is immoral in of itself? Both are injustices and both have inherent victims (the family of the original victim and the family of the condemned innocent). How do you prove one is worse than the other?

SmoothB said...

You keep conflating concepts like "immoral" and "unjust" and "bad," which is a bit odd given that you don't seem to be a pure utilitarian. I constantly fail to catch murderers. All else being equal, that's not as good as if I bagged two or three a week. But it's not immoral.

But my point was merely one of efficiency. Why are you imprisoning the guilty? If you say "because that's the right thing to do," then I'll agree, but I'll ask where that knowledge can possibly come from, given that it fails to provide information about whether it's better to presume innocence or guilt. But if you're arguing for some sort of objective, scientific explanation of the morality, then again: what's the point of imprisoning the guilty, since it doesn't undo the crime? Surely the objective, scientific answer is something along the lines of self-protection or deterrence or what have you. So, okay, doesn't that bring us back to my point?

(You could argue that we imprison the guilty not for deterrence or protective purposes but out of a sense of vengeance. And I might agree with that, but then I'd ask you how far you'd go with that and whether you're willing to hold that antipathy can be just as much of a motivator as sympathy or personal utility.)

David said...

This are important questions and I don't have very good answers for them; we've long moved away from my area of expertise and into philosophy.

The court letting a guilty man go is not the same as not looking for murderers. In the simplest way, it is not your nor my job. (You could make a "so what?" arguement and I might note the benefits of specialization, institutional norms and cost-benefit analysis; there would be an as good or better philosophical arguement to make instead but I can't pin it down right now.)

Back to your question: "what's the point of imprisoning the guilty, since it doesn't undo the crime?" Good question because I think it goes beyond deterrence. I think of it in terms of proportional response (in international law, if a country does a crappy thing to another country, that country is allowed to respond proportionally; I nuke you, you nuke me). Unless in urgent circumstances (such as self-defense) I find killing to be morally wrong so for murderers and their ilk, imprisionment is the next best thing for "eye for an eye."

It is not merely a detterent; this applies to a person's sense of justice. People gain utility when they know the bad guy lost and a way to help ensure he lost is to proportionally respond. That is what I was trying to capture: that warm feeling people get when the bad man goes to jail (even though, in GiI he is not actually a bad guy) or the disutility when the court fails to find the bad guy (even though, in IiG, they actually did). Perhaps we should include a huge disutility from the falsely accused but then we would also have to accuse a huge utility from the wrongly set free. For simplicity and scientific skepticism, I assumed that they canceled.

David said...

Oops: poor wording on my part. I meant to say the the good feelings people get of convicting an actual innocent roughly cancel the bad feelings that innocent get from going to jail.

At the same time, the good feelings a guilty gets by getting off roughly cancels the bad feelings the public gets by not getting justice.

I doubt either of these are really true though I could've sat down and tried to figure it out. I'm not sure I would be successful though if I was I suspect I would have again favored the innocent until proven guilty side anyway. I wanted to make my case without relying on something so potentially ambiguous.

Tim said...

David, I don't know if you've weighed in the fact that the victims are likely to get at least some satisfaction from the outcome no matter if the accused is actually guilty or not, so long as they are convicted - it's always more pleasant to believe that justice has been served.

If you weight their pleasure at a conviction highly enough (which would, I understand, obliterate your nicely balanced experiment), it might actually become more efficient in terms of social satisfaction to always find someone guilty of a crime.

And the situation might become much more comlpex if you start to take into account the fact that the whole trial may simply be a tool to deflect guilt from another party - others may gain a great deal of satisfaction.

It seems that we're always looking for someone to blame - gas prices rise, global warming, depletion of the ozone layer, the fact that I'm gaining/losing weight, etc. And THAT seems to be a topic worth exploring to me, no?

I'll want to look at cases of both distributed responsibility (e.g. our "responsibility" for us electing a particular politician) and cases of shifted responsibility (McDonald's made me eat the fries, really!).

Tim said...

I realize, I should say, that you were trying tyo limit the analysis to the things that everyone in society can visibly suffer or benefit from - but that's definitely not the only goal of the justice system (and I'd argue, it should become even less of one, with us letting civil courts handle these matters more than criminal courts...), and I'm not sure that that sort of analysis really bears a faithful reflection of the real court system, which always takes into some account the victims themselves.