Pasti:
Ok. Let's start with the idea that universes are just algorithms. Although that's too speculative for most physicists, it at least makes the problem mathematically well defined.
J?rgen Schmidhuber has done some recent work on this idea. He gives references and some explanations
here. I actually don't agree with most of what Schmidhuber writes there. First of all if you are considering completely general algorithms there is no need to worry about quantum mechanics not being explainable as a local deterministic theory. Also I disagree with the remarks about the Anthropic Principle. In fact he totally ignores an ''anthropic factor'' in the measures he proposes in his papers. For him this is a one or zero thing.
Schmidhuber says that you exist or you don't exist in a universe. He considers two universes with equal ''intrinsic'' measure equally likely even if you occur a million times more often in one of them. That's convenient, because then he then doesn't have to worry about how to define a (human) observer inside an algorithm and how to count them!
To understand why it is necessary to include the anthropic factor in the measure we have to look at how the Doomday Argument was resolved (although some people still don't agree with this).
Ken Olum has done some recent work on such problems. He explains
here why it is necessary to treat ''possible observers'' in the same way as ''actual observers''. In a multiverse setting this implies that you should include the anthropic factor in the measure.
On page 15 of the article he actually gives a simple argument why (once one accepts the anthropic factor), the measure of a universe should decay exponentially with the amount of information needed to specify it. This feature seems to be universal, as it is also present in the formulas given in Schmidhuber's papers. Also, you can consider the argument about running an algorithm N times as wrote earlier.
Also, note that many physicists do have an implicit notion of measure. E.g. most physicists find the occurrence of an incredibly small but nonzero cosmological constant troubling...
