Saturday, 25 September 2010

Looking for Proof


Freedom's pretty great, huh?

I’m pretty sure it is.

Maybe I’ll go and look for some more evidence today; read some articles in economics journals or something. And then I’ll be even more sure that Libertarianism’s the best. Infact, the longer I study, the more confident I’ll be. If I knew all the arguments and all the facts, I’d be absolutely confident.

...

Except that’s impossible.

Your expectation of your level of belief after the new evidence you’re going to find must be the same as your current level of belief. If there’s a big chance of becoming a little more confident, there must be a little chance of becoming a lot less confident to match it. Only one will be the case, and your level of belief will change, but you can’t know in advance which way, or how much.

If you already knew that, after reading that book, you’d be more sure of the Law of Comparative Advantage, why not just update your belief now? Afterall, you’d have evidence of evidence – and that’s as good as actually having evidence. If you expect to become more confident, or less, you should have already done so.


To say it a different way, lets suppose we represent our levels of belief using probability.

Are we allowed to do this?

We're not allowed: we have no choice. Anything else is just plain wrong, and if you do anything else you will lose.

Let H be our hypothesis, and E be some piece of evidence we’re going to look for. We can easily represent our expected level of belief in the proposition thus,

P(H|E)P(E) + P(H|¬E)P(E)

but we can break up our current level of belief in exactly the same way

P(H) = P(H and E) + P(H and ¬E)

= P(H|E)P(E) + P(H|¬E)P(¬E)

Yes: our expected new level of belief is the same as our current level. There’s a conservation of expected evidence.


So you can’t go looking for proofs of Libertarianism.

Well, ok, you can. But if you don’t find them, if it turns out to be ¬E rather than E, you have to become less confident in Libertarianism. We may be right, but we’re not magic, and the laws of probability bind us too.

1 comment:

Oliver said...

This is true!
If belief in libertarianism = belief that (free markets perform consistently better than regulated markets), for most economically-literate type libertarians it'd take a lot of evidence before regulation appears a good idea. Aggregating evidence just becomes a convenient way of being more able to convince others of one's viewpoint, rather than pushing about one's P(libertarianism==true). Perhaps, however, availability bias works at the same time to ensure that after a lot of libertarian reading, you simply don't remember the opposing evidence as strongly. [Not that it's very convincing ;)]