Tuesday, November 02, 2004

The bin Laden Tape and the Holmes-Moriarty Problem

I knew that if a new bin Laden tape emerged, people on both sides would try to spin it to support their candidate. The Bushies have been far worse about this sort of thing, in many cases straightforwardly asserting that bin Laden wants Kerry to win.

Since I believe that Bush has handled the war against al Qaeda about as badly as it could have been handled, I think that bin Laden should be rooting for Bush. But that really doesn’t matter here.

Here I’m interested in this question: what should we make of any bin Laden tape that seems to contain an explicit or implicit endorsement of either candidate? Let’s consider an explicit endorsement, since it’s easiest to think about and the same principles apply in the case of implicit or suggested endorsements.

Suppose OBL comes out and says “I want Bush to win.” What should we make of this? Certainly not that OBL wants Bush to win. OBL may be evil, but he is obviously not without a certain low cunning. He’s got to know that if he endorses Bush this helps Kerry because we Americans--though perhaps not the sharpest tools in the shed--are smart enough to figure out that if OBL wants Bush to win, that’s at least a little reason for us to want Kerry to win. So his endorsement of Bush would help Kerry.

But, of course, this game of trying to guess what the other person is thinking can be iterated forever. Recognizing that we’ll be inclined to do the opposite of what he wants, OBL should then—supposing he wants Bush to win—endorse Kerry. But, again, we're smart enough to figure out that he’s smart enough to figure that out, so we should conclude that his endorsement of Kerry is just a way of getting us to vote for Bush. And he, of course, is smart enough to figure that out, so if he really wants us to vote for Bush, then he should endorse Bush. But, again, we're smart enough to figure out what he's trying to do, so…well, you see where this is going.

This is basically a decision-theoretic problem of a kind known as a Holmes-Moriarty problem, as one version of it appears in a Sherlock Holmes story in which Holmes is trying to figure out which train station to get off at given that Moriarty is trying to catch him and so trying to figure out which station he (Holmes) will get off at.

There’s a lot of literature on this, but I’m not familiar with it. Besides, I’ve got to go give an exam now. But the rough-and-ready lesson seems to be the obvious one: you can’t—to say the least--take utterances like bin Laden’s at face value.


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