David's Sling by Marc Stiegler Page B

Betrayals of their own.
    "All in all, we have a very rational group here," Hammond says with airy cheer. "Fortunately, I think we can improve on that."
    He continues. "I always feel sorry for people encountering the Prisoners Dilemma for the first time. The Prisoner's Dilemma hurts because there is no formula for success. Intuitively, we suspect that the right answer is to Conspire, thus working together with the other prisoner for mutual gain. And if we could talk with the other prisoner, if we could communicate, we could make a good arrangement. But looking at the situation without that ability to communicate, we conclude that we must protect ourselves. The merely rational mind inevitably derives a losing formula."
    Hammond leans forward and whispers, as if conspiring with the members of the class in a secret fight with a vicious universe. "But if you can step beyond rationality to superrationality, then you can derive a winning formula. The formula only works if your partners are superrationai, too—but at least it's a winning formula sometimes. It's better than what happened to all of you in the Dilemma you just faced. " Hammond points at Bill. "What's the sum of four plus three?"
    SNAP. Bill looks up, startled. "Seven," he answers without hesitation.
    "If another person in a different room were asked the same question, would he give the same answer?"
    Bill mutters. "Of course."
    "So the two of you would be able to make that agreement without communicating?"
    "Sure," Bill snaps. "There's a formula for calculating the right answer."
    "And everybody knows the formula." Hammond looks around the class. Some look puzzled; others look expectant.
    Hammond continues. "Suppose some of the people didn't know the formula. Then you couldn't guarantee that you and the other person would get the same answer, could you?" A shiver seems to sweep the room as many people shake their heads.
    "Okay, now suppose there were a formula for deciding what to do in the Prisoner's Dilemma. No matter who you were, if you applied the formula, you would get the right answer, right? And if you knew that your partner knew the formula, you wouldn't have to worry about the outcome: you could both crank the formula and come out with the right answer."
    Hammond raises his arm and points to every person in the class. "So the very assumption that there is a formula tells us what the formula must be, does it not? If there is a formula, the formula says to Conspire, to cooperate with the other prisoner." His arm descends in a human exclamation mark. "But the formula only works if you know the formula, and if you know that your partner knows the formula, and if your partner knows that you know the formula."
    About a fourth of the faces in the class brighten immediately with understanding; others brighten more slowly as they grasp the concept. Hammond drawls, "So you and your partner must in some sense be superrational to succeed, for you must be not only rational enough to select rationally among your individual choices, you must also be rational enough to understand the meaning of rationality for the group."
    Hammond's eyes shine with pleasure in revealing the key to the game. "So the big question is, how do you find out if the other guy is as superrational as you are? In the Prisoner's Dilemma, there is one way to find out." He spreads his arms in a gesture of martyrdom. "Assume your partner knows the formula in the first round: Give him a Conspiracy. If he knows the formula, he will also give you a Conspiracy in that first round, and you will have found each other.
    "But if he doesn't give you a Conspiracy in that first round, you know that he doesn't know the formula. He may be rational as an individual, but he hasn't succeeded in looking outside his own viewpoint—he hasn't achieved superrationality, so you have to treat him accordingly. In games where your partner is only rational, or worse yet, irrational, you must betray him, for he will betray