As an aside, note that decision-theory-with-precommitments has no problem managing duplication events. That’s why I consider decision theory as the more fundamental object; probability theory is a subset of decision theory where the utility function is the Brier score or any other strictly proper scoring rule.
The utility function will also encode how to aggregate Brier scores across multiple duplicates; summing will lead to SIA-like behaviour, while averaging leads to SSA-like behaviour. In that view, a Sleeping Beauty who sums Brier scores and chooses to create a billion copies is not changing her current or future credence of tails; instead, she’s maximising her utility in the tails world.
This is also my takeaway from stuff like OSAC and Non-Realist UDASSA, where probabilities in general are much more like caring measures/utility functions than they are beliefs, and a caring measure expresses how much the agent cares about how things go in particular worlds.
This is also why contra David Matolcsi, I don’t find the subjectiveness of his solutions to be an actual problem.
Put another way, utility theory/decision theory is more general than probability theory, and the goal in those anthropic problems/acausal trade problems/decision theory problems is not to get a correct model according to a specific model of the world, but rather to maximize utility in various worlds.
This is unavoidably, irretrievably subjective, but you can learn to at least accept it as a basic precondition for doing well at these problems, even if you aesthetically dislike it.
This is also my takeaway from stuff like OSAC and Non-Realist UDASSA, where probabilities in general are much more like caring measures/utility functions than they are beliefs, and a caring measure expresses how much the agent cares about how things go in particular worlds.
This is also why contra David Matolcsi, I don’t find the subjectiveness of his solutions to be an actual problem.
Put another way, utility theory/decision theory is more general than probability theory, and the goal in those anthropic problems/acausal trade problems/decision theory problems is not to get a correct model according to a specific model of the world, but rather to maximize utility in various worlds.
This is unavoidably, irretrievably subjective, but you can learn to at least accept it as a basic precondition for doing well at these problems, even if you aesthetically dislike it.
Yep, roughly where I’m at.