You know, it's actually possible for a rational person to be unable to give consistent answers to de Finetti's choice under certain circumstances. When the person offering the bet is a semi-rational person who wants to win money and who might have unknown-to-me information, that's evidence in favor of the position they're offering to take. Because I should update in the direction of their implied beliefs no matter which side of the bet they offered me, there will be a range around my own subjective probability in which I won't want to take any bet.
Sure, when you're 100% sure that the person offering the bet is a nerd who's solely trying to honestly elicit some Bayesian subjective probability estimate, then you're safe taking either side of the same probability bet. But I'll bet your estimate of that likelihood is less than 100%.
I don't see how this applies to ciphergoth's example. In the example under consideration, the person offering you the bet cannot make money, and the person offered the bet cannot lose money. The question is, "For which of two events would you like to be paid some set amount of money, say $5, in case it occurs?" One of the events is that a fair coin flip comes up heads. The other is an ordinary one-off occurrence, like the election of Obama in 2012 or the sun exploding tomorrow.
The goal is to elicit the degree of belief that the person has in the ...
http://xkcd.com/1132/
Is this a fair representation of frequentists versus bayesians? I feel like every time the topic comes up, 'Bayesian statistics' is an applause light for me, and I'm not sure why I'm supposed to be applauding.