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Vladimir_Nesov comments on Remind Physicalists They're Physicalists - Less Wrong
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Free will still only makes sense when there's uncertainty about what's going on (that is resolved by your decisions), which is mostly interchangeable with there being many possible worlds (in your model), but if there are many (actual) worlds and no uncertainty (or only uncertainty independent of your decisions), free will doesn't happen.
In other words, many-worlds don't change anything about free will, in either direction. And to support free will, even a single branch must appear as a collection of possibilities that can't be ruled out.
Many-worlds doesn't change anything about free will, but it does (under some interpretations) change the answer to the question "could you have said anything else than what you did say in the next moment?"
This sense of "could" seems mostly unrelated to the decision-theoretic "could", so the answer to the question changes only to the extent there's equivocation for the word.
OTOH, physical indeterminism does change something about free will.
Yeah, it makes your actions random rather than predictable. A massive improvement!