Wednesday, 12 May 2010

Gladwell on probability

There's quite a nice list of random quotes from Malcolm Gladwell in an interview for this Sunday's Observer.

However, one of them seems to show some misunderstanding of probability:
History suggests that there is almost exactly a 50% chance that any piece of information a spy gives you is true. We would be as well off getting rid of the secret service and flipping coins.
Now if the first part of this sentence is true (which I have no reason to doubt) the second part most definitely does not follow. This is (tangentially) related to a discussion that's been going on at Peter Cameron's blog about probability. Unless spies only ever make statements about things where your prior was already 50%, a 50% accuracy rate could be incredibly useful.

Eg, let's say we're trying to find out where a particular terrorist group has their headquarters. To start with, our probabilities are essentially uniformly distributed across the whole of the world. Our spy comes up to us and says 'the HQ is at number 32 Barkston Gardens, Earl's Court, London'. This information is far from useless - in fact, if we have more than one spy coincide on the same piece of information then we're in business, and can find the location pretty quickly.

Of course, I think Gladwell's '50%' is actually just a proxy for 'exactly as true as you'd expect if they were generating their statements at random', but that's not *quite* the same thing

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