I haverepeatedlyargued for a departure from pure Bayesianism that I call "quasi-Bayesianism". But, coming from a LessWrong-ish background, it might be hard to wrap your head around the fact Bayesianism is somehow deficient. So, here's another way to understand it, using Bayesianism's own favorite trick: Dutch booking!

Consider a Bayesian agent Alice. Since Alice is Bayesian, ey never randomize: ey just follow a Bayes-optimal policy for eir prior, and such a policy can always be chosen to be deterministic. Moreover, Alice always accepts a bet if ey can cho

And here I thought the reason was going to be that Bayesianism doesn't appear to include the cost of computation. (Thus, the usual dutch book arguments should be adjusted so that "optimal betting" does not leave one worse off for having payed, say, an oracle, too much for computation.)

3Dagon14dBayeseans are allowed to understand that there are agents with better estimates
than they have. And that being offered a bet _IS_ evidence that the other agent
THINKS they have an advantage.
Randomization (aka "mixed strategy") is well-understood as the rational move in
games where opponents are predicting your choices. I have read nothing that
would even hint that it's unavailable to Bayesean agents. The relevant
probability (updated per Bayes's Rule) would be "is my counterpart trying to
minimize my payout based on my choices".
edit: I realize you may be using a different definition of "bayeseanism" than I
am. I'm thinking humans striving for rational choices, which perforce includes
the knowledge of incomplete computation and imperfect knowledge. Naive agents
can be imagined that don't have this complexity. Those guys are stuck, and
Omega's gonna pwn them.

4mr-hire14dIt feels like there's better words for this like rationality, whereas
bayesianism is a more specific philosophy about how best to represent and update
beliefs.

I have repeatedly argued for a departure from pure Bayesianism that I call "quasi-Bayesianism". But, coming from a LessWrong-ish background, it might be hard to wrap your head around the fact Bayesianism is somehow deficient. So, here's another way to understand it, using Bayesianism's own favorite trick: Dutch booking!

Consider a Bayesian agent Alice. Since Alice is Bayesian, ey never randomize: ey just follow a Bayes-optimal policy for eir prior, and such a policy can always be chosen to be deterministic. Moreover, Alice always accepts a bet if ey can cho

... (read more)And here I thought the reason was going to be that Bayesianism doesn't appear to include the cost of computation. (Thus, the usual dutch book arguments should be adjusted so that "optimal betting" does not leave one worse off for having payed, say, an oracle, too much for computation.)