I don't think there's anything more to be done in the cause of explaining the mechanism. We did explain the mechanism, self-locating uncertainty when the wave function branches. That's the mechanism. I suspect that your thought that we haven't explained the mechanism is a relic of the thought that if you have probabilities, they have to reduce at some point to literally counting. The thing about many worlds is, let's not over-complicate this. It is crystal 100% superduper clear that if you think that the theory implies any probability rule at all, that probability rule is going to be the born rule.
Welcome to the November 2022 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!
Support Mindscape on Patreon.
See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.