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Flunking The Prisoners’ Dilemma

Lawrence Crocker considers how best to avoid a lengthy prison term.

Dear Joe,

So there we were, you and I, waiting for the converted school bus with the chain link windows that would transport us to our five years in U.S. federal prison. I will not revisit the details of our once-thriving securities business. We prided ourselves on our creative ‘client/market positioning’, even if the unimaginative prosecutors contended it was a scheme to defraud.

I know it’s not much pleasanter to recall the circumstances that led to our final five year pleas. The only good thing to be said about our plea agreements is that we might have done a lot worse after trial. Like 90% of U.S. defendants, we didn’t want to take the risk. Prosecutors give attractive enough deals to get the job done – attractive enough that even completely innocent people sometimes take them. I looked up what the U.S. Constitution has to say about plea bargaining. It’s in Article III, Section 2: “The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury.” (You and I weren’t impeached!) I know that we waived our rights to a jury trial. They had us go through quite a song and dance in court about how we were giving up our rights knowingly and voluntarily. But did the federal court have a constitutional power to convict us on pleas? Article III is the only place the federal courts get their power, and it doesn’t look as if they were given any to dispose of criminal cases except by jury trial. This makes me wonder why constitutional textualists like Justice Scalia aren’t all over plea bargaining. But then I guess he would pull out the other part of his interpretational philosophy – ‘the traditions of the American people’. That’s a handy way for conservatives to get the result they want when the text is against them. Not that what we did was necessarily all that innocent. We knew we were skating a little close to the line. But I wish we could have had something more than the prosecutors’ assurance that we went over the line. Our defense lawyer wasn’t much help: “You have triable issues, but I can’t give you a guarantee.” Great!

Had to get that off my chest, but it’s not the reason I’m writing you. What has been bugging me is the way the plea bargain worked. Doesn’t it eat at you that we would have done only one year each on a record-keeping count if neither one of us had confessed and implicated the other?

I suppose we can take some comfort from the fact that we were caught in a literal version of the famous ‘prisoners’ dilemma’. As the prosecutors made it clear, if either of us ratted out the other, who did not confess, then the co-operator would get off free while the holdout would do ten years. If we both confessed (as we did in the end), we have would each got five years; and if neither confessed, one year apiece.

My ActionYour ActionMy SentenceYour Sentence
Confess Confess 5 5
Confess Holdout 0 10
Holdout Confess 10 0
Holdout Holdout 1 1

The economists and philosophers find versions of the prisoners’ dilemma everywhere. Pepsi and Coke are said to spend millions on advertising to hold market share against each other because of a marketing version of the prisoners’ dilemma. It’s the darling of decision theory. Well I can tell the theorists that when you’re face to face with the dilemma in real life, its mathematical and philosophical elegance loses all its charm.

What bothers me most was the story of those two other convicts we talked to while we were in the holding cell waiting for that prison bus. You will recall them – they were from some remote village in central Africa, although I can’t remember the country – and they had been subjected to the same kind of questioning and deal as us, but they were heading to jail for only one year sentences.

At first we did not believe that they had beaten the prisoners’ dilemma, but they gave us the blow by blow details. Their situation was just like ours : 0/10 if one snitched and the other held out, 5/5 if both confessed, or 1/1 if neither did. I immediately surmised that these villagers must have cared too much for each other to have followed our self-interested strategy of confessing and implicating the other. I said something about the cash value of the precept that “Ye shall love one another.” But one of the Africans interrupted me with a vehement speech about his antipathy towards his fellow: “Our families have been enemies since before there was time. I worked with him only because I knew no one else here. The prospect of his spending ten years in prison would have made my freedom doubly sweet.”

Puzzled, you asked them how, then, neither of them confessed. The response, which one gave and the other corroborated with nods, went something like this, I remember:

“I saw at once that, just as I favored the 0-10 result, he would favor the 10-0. So the 0-10 result would not happen, and 5-5 loomed. I wanted none of that. Was there, then, any possible way to reach 1-1? I thought, if only they had not taken the tiny two way radios we had used in our work, then we could coordinate our tactics. We could hear each other refuse to confess. Betrayal would bring retaliation, and 5-5. But, of course, they had taken away our radios, and our separate cells were too far apart to communicate anything. Then it occurred to me that I knew exactly how each of us would behave if we had the radios. We would steadfastly refuse to confess from beginning to end. It’s not the presence of the radio, but the determination to stick to this conduct that would assure the 1-1 result. We did not have to communicate any information at all. I knew what I had to do, and I knew that he would too, because I could be sure that he would think just as I did. We are enemies, but we are products of the same little village. I know how he thinks as well as I know myself.

“Having reached the conclusion that simulated radio would give just as good coordination as a real radio, I had to consider the weakness of simulated radios: they can’t give actual information of betrayal. What if, having realized the advantages of simulated coordination, he concludes that I will not confess – would he not, then, have gleefully confessed, obtaining the 0-10 solution for himself? But were he to conclude that this was his rational strategy, he would know that I would conclude so as well, so this strategy would not produce 0-10, but 5-5. He knew that I would have gone through the same reasoning. So the simulated coordination strategy ruled out betrayal, whether premeditated or as a last-minute afterthought. Betrayal is simply not a permitted move on the only strategy that will work. Once I was confident that this was the right strategy, I became confident that my enemy would realize it with the same confidence. So I did not confess, and neither did he.”

I nearly shouted in my impatience at his naiveté: “But nothing stopped you from doing the rational thing and confessing, hanging your enemy out to dry!”

Do you remember how he calmly responded, “For which of us would that have been rational?”

“Well, for both of you, of course.”

“And then we would be serving five years, like you.”

“Yes, but at least you would have done the rational thing!”

He replied, “Perhaps in our backward country we do not properly understand rationality. We simply think of it as following the best path to get where you want to go.”

During these years at prison, I have had a lot of time to think about those villagers. Surely it can’t be that ‘simulated radio coordination’ is really a solution to the prisoners’ dilemma? After all, if I had tried it, I would now be doing ten years. So was the success of the Africans due to their strategy, or rather to the fact that they knew each other so well that they could be confident that one would perfectly reflect the other? If I knew that you would do just what I did – if for example I could force you to mimic me – then of course I would not have confessed either. The 10-0 boxes would disappear, and I would have chosen 1-1 instead of 5-5.

The Africans had no causal effect on each other. Each merely correctly predicted the other, just as you and I each, correctly and unhappily, predicted that the other would confess. Had I even entertained the simulated radio strategy, I would have rejected it because I knew that you would regard such a solution as irrational without a check against betrayal. What the Africans knew about each other, in the end, was only the same thing that you and I knew about each other – the way we would assess the rationality of a strategy. By their lights the simulated radio strategy was rational. Each knew that the other would regard it as rational. And it is hard to say that they were proved to have an inferior notion of rationality to our own.



© Dr Lawrence Crocker 2009

Lawrence Crocker is an ex-lawyer and ex-law lecturer, and now teaches philosophy at Dartmouth College, in New Hampshire.

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