Abstract: If we assume that any universe can be modeled as a computer program which has been running for finitely many steps, then we can assign a multiverse-address to every event by combining its world-program with the number of steps into the world-program where it occurs. We define a probability distribution over multiverse-addresses called a Finite Occamian Multiverse (FOM). FOMs assign negligible probability mass to being a Boltzmann brain or to being in a universes that implements the Many Worlds Interpretation of quantum mechanics.

One explanation of existence is the Tegmark level 4 multiverse, the idea that all coherent mathematical structures exist, and our universe is one of them. To make this meaningful, we must add a probability distribution over mathematical structures, effectively assigning each a degree of existence. Assume that the universe we live in can be fully modeled as a computer program, and that that program, and the number of steps it's been running for, are both finite. (Note that it's not clear whether our universe is finite or infinite; our universe is either spatially infinite, or expanding outwards at a rate greater than or equal to the speed of light, but there's no observation we could make inside the universe that would distinguish these two possibilities.) Call the program that implements our universe a world-program, W.  This could be implemented in any programming language - it doesn't really matter which, since we can translate between languages by prepending some stuff to translate.

Now, suppose we choose a particular event in the universe - an atom emitting a photon, say - and we want to find a corresponding operation in the world-program. We could, in principle, run W until it starts working on the part of spacetime we care about, and count the steps. Call the number of steps leading up to this event T. Taken together, the pair (W,T) uniquely identifies a place, not just in the universe, but in the space of all possible universes. Call any such pair (W,T) a multiverse-address.

Now, suppose we observe an event. What should be our prior probability distribution over multiverse-addresses for that event? That is, for a given event (W,T), what is P(W=X and T=Y)?