The Economics Of Heroism

It's a scene from a dozen westerns. A lynch mob has gathered outside the jail, determined to take a prisoner from the sherrif and hang him without a trial. The sheriff stands coolly before them and tells them they're won't be any hanging tonight, at least not so long as he's got his shotgun and his Colts.

"You can't kill all of us, sherrif," a rowdy declares.

"I don't mean to kill all of you," the sheriff inevitably replies. "I just mean to kill the first three men that move on me. So who's it gonna be? You? You? You?"

As no one's willing to be part of the first wave that gets gunned down, the crowd disperses, defeated.

That's the Prisoner's Dilemma in the old west. The Prisoner's Dilemma is an economic notion that notes that people, lacking perfect information about how other similarly-situated people might act, choose frequently to act against their own best interests.

Two suspects are held in two different interrogation tanks. The police suspect they're guilty of armed robbery and murder but can't prove it without a confession. Both suspects know this -- so they know their best "move" in the "game" is to keep silent and say nothing.

But that's only their best move if they know for a fact their confederate isn't talking and blaming the other for the crime. If Confderate 2 is spilling to the cops and trying to pin the blame on Confederate 1, then Confederate 1's actual best move is to do similarly, and implicate Confederate 2, so at least Confederate 2 will get the bulk of the punishment whereas Confederate 1 will get a deal and a lesser sentence.

Both men would do better to stay silent. Both men know that. But as neither man has good information about what the other is actually doing, they both tend to spill and implicate the other. Result? Due to imperfect information, they both take a suboptimal course of action that guarantees both some time in jail.

Given a psychopathic gunman, it's probably true that a group of six or ten men could all rush him at once. If any one of them rushed him alone, his chance of survival would be somewhere around 10% or less -- he'd almost certainly die.

But acting as a group, the odds of survival zoom to a respectable 75% or even higher. The gunman, after all, can only shoot so many of them as the group charges towards him; after bringing one or two down, the rest will slam him to the ground and begin beating him to death.

But the Prisoner's Dilemma is at work here, too. Yes, assuming perfect information, and assuming that each man takes the course of action that is best for all concerned, they can all act heroically and yet with fair chance of survival and success.

But what if they don't have perfect information? What if they can't trust that each man will take the best course of action for the entire group?

Let's face it: The first man to charge, the one out in front, is the one most likely to be the gunman's main target. The gunman will only stop firing at that target after he's killed him or at least dropped him to the ground; then he'll move on to the second closest (and hence second most threatening) target.

If all men chage simulatenously, they will most likely be successful, and most of them -- perhaps all of them, will live.

But what if they don't? What if some men attempt to lag behind in order to make themselves lesser threats -- trying to be part of the safer "second wave" rather than the shared simultaneous first wave as agreed upon?

Or worse yet, what if some men deliberately step behind another man to use his ally as cover?

Or worst of all, what if some men simply never charge at all but remain behind cover due to a failure of nerve or a cynical desire to let the others take the bullets and attack the shooter only once he's forced to reload?

In economic terms: What if one suspects that many of one's allies intend to be "free riders" on one's own heroism and embrace of jeopardy? What if one suspects that when "Let's roll!" is called out, one might be the only one breaking cover at all?

The net result: While it may be true that all men here have an optimal solution to their shared problem, a lack of trust in their allies to act according to this optimal solution compels many of them, if not all of them, to elect a decidedly suboptimal solution -- not doing anything at all and just hoping for the best.

There is of course an organization that attempts to eliminate the Prisoner's Dilemma from group action in combat. That organization is of course the US military (and all other world militaries, for that matter). By making cowardice a crime punishable by imprisonment or even death, by drilling constantly with one's allies so that one achieves nearly perfect information about their intentions, capabilities, and likely behaviors under fire (i.e., they won't shirk and lag behind allowing their friends to assume all the risk themselves), etc., the military seeks to push men to take the optimal choice -- coordinated group action with all sharing about the same level of risk -- rather than each selecting the suboptimal choice, all men cringing in a trench hoping not to be killed, paralyzed for lack of confidence their fellow fighters will be doing anything apart from cringing themselves.

Given the fact that the VaTech students are almost overwhelmingly not so trained, it's hardly surprising so many selected the decidedly suboptimal choice even with a killer picking them off one by one in a room. Do nothing, and there's a chance -- a chance -- he'll run out of bullets, run out of interest, or run into a SWAT team before he gets to you.

Do something -- and do it alone -- and you're almost guaranteed to be killed before you take your third step towards him.

If they could properly coordinate together, and quickly establish sufficient confidence in each other that the coordinated charge would be selected by each man, they could have an optimal outcome. But they can't do that -- resulting in passivity, tragedy, and a worse outcome than was technically necessary.

Let me make a quick political point: Schools ought to increase their ROTC programs just so they have a sufficient number of men trained and willing to select the optimal "move" in a deadly game.

Because this is just not going to stop. Ever.

posted by Ace at 04:16 PM

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