(Note that Bayes-with-a-side-channel does not imply conditions such as convergence and calibration; so, Jeffrey’s theory of rationality is more demanding.)
What about the converse? Is a radical probabilist always behaviorally equivalent to a Bayesian with a side-channel? Or to some sequence of virtual evidence updates?
You seem to say so later on—“And remember, every update is a Bayesian update, with the right virtual evidence”—but I don’t think this was proven?
Ah, this was supposed to have been established in the section “Representing Fluid Updates”—the idea being that any change in probabilities can be represented as virtual evidence on a sufficiently fine partition (barring an update from zero to a positive number).
What about the converse? Is a radical probabilist always behaviorally equivalent to a Bayesian with a side-channel? Or to some sequence of virtual evidence updates?
You seem to say so later on—“And remember, every update is a Bayesian update, with the right virtual evidence”—but I don’t think this was proven?
Ah, this was supposed to have been established in the section “Representing Fluid Updates”—the idea being that any change in probabilities can be represented as virtual evidence on a sufficiently fine partition (barring an update from zero to a positive number).
Ah, I see. Made sense on a second read. Thanks.