“Bayesianism’s coherence and uniqueness proofs cut both ways. Just as any calculation that obeys Cox’s coherency axioms (or any of the many reformulations and generalizations) must map onto probabilities, so too, anything that is not Bayesian must fail one of the coherency tests. This, in turn, opens you to punishments like Dutch-booking (accepting combinations of bets that are sure losses, or rejecting combinations of bets that are sure gains).”
I’ve never understood why I should be concerned about dynamic Dutch books (which are the justification for conditionalization, i.e., the Bayesian update). I can understand how static Dutch books are relevant to finding out the truth: I don’t want my description of the truth to be inconsistent. But a dynamic Dutch book (in the gambling context) is a way that someone can exploit the combination of my belief at time (t) and my belief at time (t+1) to get something out of me, which doesn’t seem like it should carry over to the context of trying to find out the truth. When I want to find the truth, I simply want to have the best possible belief in the present—at time (t+1) -- so why should “money” I’ve “lost” at time (t) be relevant?
Perhaps I simply want to avoid getting screwed in life by falling into the equivalents of Dutch books in real, non-gambling-related situations. But if that’s the argument, it should depend on how frequently such situations actually crop up—the mere existence of a Dutch book shouldn’t matter if life is never going to make me take it. Why should my entire notion of rationality be based on avoiding one particular—perhaps rare—type of misfortune? On the other hand, if the argument is that falling for dynamic Dutch books constitutes “irrationality” in some direct intuitive sense (the same way that falling for static Dutch books does), then I’m not getting it.
“Bayesianism’s coherence and uniqueness proofs cut both ways. Just as any calculation that obeys Cox’s coherency axioms (or any of the many reformulations and generalizations) must map onto probabilities, so too, anything that is not Bayesian must fail one of the coherency tests. This, in turn, opens you to punishments like Dutch-booking (accepting combinations of bets that are sure losses, or rejecting combinations of bets that are sure gains).”
I’ve never understood why I should be concerned about dynamic Dutch books (which are the justification for conditionalization, i.e., the Bayesian update). I can understand how static Dutch books are relevant to finding out the truth: I don’t want my description of the truth to be inconsistent. But a dynamic Dutch book (in the gambling context) is a way that someone can exploit the combination of my belief at time (t) and my belief at time (t+1) to get something out of me, which doesn’t seem like it should carry over to the context of trying to find out the truth. When I want to find the truth, I simply want to have the best possible belief in the present—at time (t+1) -- so why should “money” I’ve “lost” at time (t) be relevant?
Perhaps I simply want to avoid getting screwed in life by falling into the equivalents of Dutch books in real, non-gambling-related situations. But if that’s the argument, it should depend on how frequently such situations actually crop up—the mere existence of a Dutch book shouldn’t matter if life is never going to make me take it. Why should my entire notion of rationality be based on avoiding one particular—perhaps rare—type of misfortune? On the other hand, if the argument is that falling for dynamic Dutch books constitutes “irrationality” in some direct intuitive sense (the same way that falling for static Dutch books does), then I’m not getting it.