Nevermind. I had it in mind that un-dutch-bookability was a property of perfect Bayesianism alone—so that in the way that all other methods are approximations of Bayes, plus or minus some constant, or restricted in some way, these departures from Bayes would open up non-Bayes systems to some incorrect calculation of probabilities, and so it would be possible to set up a situation where their calculation departs from Bayes in a systematic way, and then set up a Dutch book diachronically. It seems like you might be able to do this for frequentism, but it turns out that there are other, non-Bayes systems that are immune to Dutch books as well.
It seems like building a bet that only a Bayesian system wouldn’t get Dutch-booked on might be possible.
Hmm. What exactly do you mean?
Nevermind. I had it in mind that un-dutch-bookability was a property of perfect Bayesianism alone—so that in the way that all other methods are approximations of Bayes, plus or minus some constant, or restricted in some way, these departures from Bayes would open up non-Bayes systems to some incorrect calculation of probabilities, and so it would be possible to set up a situation where their calculation departs from Bayes in a systematic way, and then set up a Dutch book diachronically. It seems like you might be able to do this for frequentism, but it turns out that there are other, non-Bayes systems that are immune to Dutch books as well.