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Is it rational to give in to irrationality? July 24, 2010

Posted by Ezra Resnick in Game theory, Politics, Reason.
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Reuben and Shimon are placed into a small room with a suitcase containing $100,000 of cash. The owner of the suitcase offers them the following: “I’ll give you all the money in the suitcase, but only on the condition that you negotiate and reach an amicable agreement on its division. That’s the only way I will give you the money.”

Reuben, who is a rational person, appreciates the golden opportunity presented to him and turns to Shimon with the obvious suggestion: “Come, you take half the amount, I’ll take the other half, and each of us will go away with $50,000.” To his surprise, Shimon, with a serious look on his face and a determined voice says: “Listen, I do not know what your intentions are with the money, but I’m not leaving this room with less than $90,000. Take it or leave it. I’m fully prepared to go home with nothing.”

Reuben can not believe his ears. What happened to Shimon? he thinks to himself. Why should he get 90%, and I only 10%? He decides to try to talk to Shimon. “Come, be reasonable,” he pleads. “We’re both in this together, and we both want the money. Come let’s share the amount equally and we’ll both come out ahead.”

But the reasoned explanation of his friend does not seem to register on Shimon. He listens attentively to Reuben’s words, but then declares even more emphatically, “There is nothing to discuss. 90-10 or nothing, that’s my final offer!” Reuben’s face turns red with anger. He wants to smack Shimon across his face, but soon reconsiders. He realizes that Shimon is determined to leave with the majority of the money, and that the only way for him to leave the room with any money is to surrender to Shimon’s blackmail. He straightens his clothes, pulls out a wad of bills from the suitcase in the amount of $10,000, shakes hands with Shimon and leaves the room looking forlorn.

Robert Aumann calls this the blackmailer paradox, or the paradox of the extortionist. It is seemingly a paradox because the rational person gets less than the irrational person, suggesting that the most rational thing you can do is be irrational. Aumann takes this as a model for Israeli-Arab negotiations:

Twenty years ago, a brigadier general came here, maybe a major general, who didn’t identify himself. He wanted to talk to me about the negotiations with Syria. He said to me: ‘You know, Prof. Aumann, the Syrians will not give up a single centimeter of land and the reason is that the land is holy for them. Therefore, they will not concede.’ Then I told him about the extortionist. I said to him: ‘The Syrians have succeeded in convincing you because first they convinced themselves.’

What is our problem? That nothing is holy. We don’t manage to convince ourselves that anything is sacred. Not Jerusalem, not the right of return, not even Tel Aviv. We will be prepared to negotiate, and in the end even to give up Tel Aviv. We are rational as can be, and that’s our problem. . . .

There isn’t anything that we can convince the other side is sacred to us, that we’re willing to ‘be killed for it, rather than transgress.’ If there were something like that, then we wouldn’t be in the situation we are in today.

Before considering Aumann’s proposed solution, let us concede that there is indeed a serious problem here which is too often overlooked: the problem of negotiating with someone who is utterly dogmatic and inflexible. If there is truly no evidence or argument that would ever cause our opponent to change his position, then there is no point in talking to him at all, and we will just have to work around him as best we can. Suppose for a moment that the extortionist Shimon is not a human being, but rather a computer, programmed to accept only those divisions where Reuben gets no more than 10% of the money. Should Reuben attempt to argue with the computer screen, trying to convince it to be reasonable? Clearly not. The rational thing to do in such a case is to take the $10,000 and leave, and there is no paradox. The original scenario feels paradoxical because we expect people not to behave like computers, but rather to be reasonable and open to argument. The scary thing, which many good-intentioned people overlook (at their peril), is that there are human beings who have essentially made themselves into robots following a program: people who have surrendered their mind so completely to dogma that they are incapable of entertaining any alternate positions, even for a moment.

What does Aumann suggest we do when faced with such a dogmatic opponent? Apparently, he thinks we should be more dogmatic ourselves! We must distinguish, of course, between genuine dogmatism and “bluffing:” it may be a clever negotiating tactic to initially feign inflexibility so as to improve your end of the bargain, like hagglers in a market. But it seems that Aumann goes further than this, insisting that we must start by convincing ourselves that our goals are “holy” and “sacred.” Some things may indeed be nonnegotiable and worth dying for, but we need to think very carefully about what those things are, and not mimic the dogmatism of our opponents. Aumann’s proposition seems wrong both as a matter of principle and of practice. Take the issue of Jerusalem, for instance. Is maintaining Israeli sovereignty over all of Jerusalem a cause worth dying for? Is it even a just cause? I see no rational basis for such claims. And even if we did convince ourselves that we’re willing to “be killed for it, rather than transgress,” assuming that the other side is just as dogmatic, how exactly is this going to lead to any kind of solution? Even in the face of irrationality, giving up your own rationality is never the answer – even if it somehow allows you to win a battle, you will have lost the war.

This doesn’t mean we should give in to every demand of an extortionist. When placed in the blackmailer paradox against a computer, it makes sense for Reuben to take the $10,000 because that is better for him than getting nothing; however, if the computer demands that Reuben pay an additional $200,000 out of his own pocket, Reuben would have no reason to comply. If giving the extortionist what he wants is worse for us than the alternative, as it often is, then the rational course of action is to turn him down and do the best we can without him. It’s also important to remember that in real life, we usually find ourselves interacting with the same players over and over, so it may be rational for Reuben to leave the first encounter with nothing in order to make Shimon more likely to cooperate in future encounters. This, of course, assumes that Shimon is rational and is capable of changing his original strategy; against absolute dogmatism, unilateral action may be the only option. And in extreme cases, the only alternative to conversation is force. There is no room for negotiation with a suicide bomber.

Dogmatism is a very serious problem, and we must be willing to use force against it when necessary. More importantly, though, we must fight the foundations of dogmatism by promoting rationality, critical thinking, and the free flow of ideas. Not by becoming dogmatists ourselves.

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Comments»

1. Reshef Meir - July 28, 2010

What you said about Jerusalem is related to a dilemma that faced Eshkol in ’67 during the war (according to Tom Segev):
The army has already occupied most of the west bank, and pressed Eshkol to take the old city. The plan (from before the war) was not to hold on to the west bank, as this (according to government’s protocols) would jeopardize the Jewish majority, increase national Palestinian feelings, etc.
Eshkol knew that once the old city would be in Israeli hands, no prime minister will ever have enough public credit to re-divide it. Moreover, he knew that Jordan would never agree to take the west bank as part of a peace treaty, without Jerusalem.
Thus occupying the old city means getting stuck with the west bank forever (or at least have to deal with the Palestinians instead of with Jordan).
Eshkol’s (rational) conclusion was that the old city should *not* be occupied. Nevertheless, the great enthusiasm of the military success (along with the chance to shadow Ben-Gurion) engulfed him as well, and he approved the action.


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