JGWeissman comments on Bayesian Utility: Representing Preference by Probability Measures - Less Wrong
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Any action can be identified with a set of outcomes consistent with the action. See my reply to JGWeissman.
Is the example after mixing unclear? In what way?
However, the ratios of the conditional probabilities of those outcomes, given that you take a certain action, will not always equal the rations of the unconditional probabilities, as in your formula.