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.