## LESSWRONGLW

But in the infinite series of possibilities summing to 1, why should the hypotheses with the highest probability be the ones with the lowest complexity, as opposed to having each consecutive hypothesis having an arbitrary complexity level?

gjm's explanation is correct.

3gjm4yAlmost all hypotheses have high complexity. Therefore most high-complexity hypotheses must have low probability. (To put it differently: let p(n) be the total probability of all hypotheses with complexity n, where I assume we've defined complexity in some way that makes it always a positive integer. Then the sum of the p(n) converges, which implies that the p(n) tend to 0. So for large n the total probability of all hypotheses of complexity n must be small, never mind the probability of any particular one.) Note: all this tells you only about what happens in the limit. It's all consistent with there being some particular high-complexity hypotheses with high probability.