Also, it’s unclear to me how this approach relates to Bayesian conditioning.
To me, proof-based UDT is a simple framework that includes probabilistic/Bayesian reasoning as a special case. For example, if the world is deterministic except for a single coinflip, you specify a preference ordering on pairs of outcomes of two deterministic worlds. Fairness or non-fairness of the coinflip will be encoded into the ordering, so the decision can be based on completely deterministic reasoning. All probabilistic situations can be recast in this way. That’s what UDT folks mean by “probability as caring”.
It’s really cool that UDT lets you encode any setup with probability, prediction, precommitment etc. into a few (complicated and self-referential) sentences in PA or GL that are guaranteed to have truth values. And since GL is decidable, you can even write a program that will solve all such problems for you.
To me, proof-based UDT is a simple framework that includes probabilistic/Bayesian reasoning as a special case. For example, if the world is deterministic except for a single coinflip, you specify a preference ordering on pairs of outcomes of two deterministic worlds. Fairness or non-fairness of the coinflip will be encoded into the ordering, so the decision can be based on completely deterministic reasoning. All probabilistic situations can be recast in this way. That’s what UDT folks mean by “probability as caring”.
It’s really cool that UDT lets you encode any setup with probability, prediction, precommitment etc. into a few (complicated and self-referential) sentences in PA or GL that are guaranteed to have truth values. And since GL is decidable, you can even write a program that will solve all such problems for you.