As near as I can figure, the corresponding state of affairs to a complexity+leverage prior improbability would be a Tegmark Level IV multiverse in which each reality got an amount of magical-reality-fluid corresponding to the complexity of its program (1/2 to the power of its Kolmogorov complexity) and then this magical-reality-fluid had to be divided among all the causal elements within that universe - if you contain 3↑↑↑3 causal nodes, then each node can only get 1/3↑↑↑3 of the total realness of that universe.

The difference between this and average utilitarianism is that we divide the probability by the hypothesis size, rather than dividing the utility by that size. The closeness of the two seems a bit surprising.

Robin Hanson has suggested that the logic of a leverage penalty should stem from the general improbability of individuals being in a unique position to affect many others (which is why I called it a leverage penalty). At most 10 out of 3↑↑↑3 people can ever be in a position to be "solely responsible" for the fate of 3↑↑↑3 people if "solely responsible" is taken to imply a causal chain that goes through no more than 10 people's decisions; i.e. at most 10 people can ever be solely10 responsible for any given event.

This bothers me because it seems like frequentist anthropic reasoning similar to the Doomsday argument. I'm not saying I know what the correct version should be, but assuming that we can use a uniform distribution and get nice results feels like the same mistake as the principle of indifference (and more sophisticated variations that often worked surprisingly well as an epistemic theory for finite cases). Things like Solomonoff distributions are more flexible...

(As for infinite causal graphs, well, if problems arise only when introducing infinity, maybe it's infinity that has the problem.)

The problem goes away of we try to employ a universal distribution for the reality fluid, rather than a uniform one. (This does not make that a good idea, necessarily.)

This setup is not entirely implausible because the Born probabilities in our own universe look like they might behave like this sort of magical-reality-fluid - quantum amplitude flowing between configurations in a way that preserves the total amount of realness while dividing it between worlds - and perhaps every other part of the multiverse must necessarily work the same way for some reason.

If we try to use universal-distribution reality-fluid instead, we would expect to continue to see the same sort of distribution we had seen in the past: we would believe that we went down a path where the reality fluid concentrated into the Born probabilities, but other quantum paths which would be very improbable according to the Born probabilities may get high probability from some other rule.