I was thinking of the simpler case of someone who has already assigned utilities as required by the VNM axioms for the noncontroversial case of gambling with probabilities that are relative frequencies, but refuses on philosophical grounds to apply the expected utility decision procedure to other kinds of uncertainty.
(I do think the statement still stands in general. I don’t have a complete proof but Savage’s axioms get most of the way there.)
On the thread cited I gave a three state, two outcome counterexample to P2 which does just that. Having two outcomes obviously a utility function is not an issue. (It can be extended it with an arbitrary number of “fair coins” for example to satisfy P6, which covers your actual frequency requirement here)
My weak claim is that it is not vulnerable to “Dutch-book-type” arguments. My strong claim is that this behaviour is reasonable, even rational. The strong claim is being disputed on that thread. And of course we haven’t agreed on any prior definition of reasonable or rational. But nobody has attempted to Dutch book me, and the weak claim is all that is needed to contradict your claim here.
Anyone who bases decisions on a non-Bayesian model of uncertainty that is not equivalent to Bayesianism with some prior is vulnerable to Dutch books.
It seems not. Sniffnoy’s recent thread asked the very question as to whether Savage’s axioms could really be justified by dutch book arguments.
I was thinking of the simpler case of someone who has already assigned utilities as required by the VNM axioms for the noncontroversial case of gambling with probabilities that are relative frequencies, but refuses on philosophical grounds to apply the expected utility decision procedure to other kinds of uncertainty.
(I do think the statement still stands in general. I don’t have a complete proof but Savage’s axioms get most of the way there.)
On the thread cited I gave a three state, two outcome counterexample to P2 which does just that. Having two outcomes obviously a utility function is not an issue. (It can be extended it with an arbitrary number of “fair coins” for example to satisfy P6, which covers your actual frequency requirement here)
My weak claim is that it is not vulnerable to “Dutch-book-type” arguments. My strong claim is that this behaviour is reasonable, even rational. The strong claim is being disputed on that thread. And of course we haven’t agreed on any prior definition of reasonable or rational. But nobody has attempted to Dutch book me, and the weak claim is all that is needed to contradict your claim here.
Sorry, I didn’t check that thread for posts by you. I replied there.