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gjm comments on A summary of Savage's foundations for probability and utility. - Less Wrong
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Yes, that's a good way of looking at it.
If we (1) look at the way our preferences actually are and (2) consider "aargh, conflict of incommensurable values, can't decide" to be a kind of indifference, then indifference certainly isn't transitive. But, again, maybe we'd do better to consider idealized agents that don't have such confusions.
In particular because agents which do have such confusions should leave money on the table -- they are incapable of dutch-booking people who can be dutch-booked.
How so? (It looks to me as though the ability to dutch-book someone dutch-book-able doesn't depend at all on one's value system. In particular, the individual transactions that go to make up the d.b. don't need to be of positive utility on their own, because the dutch-book-er knows that the dutch-book-ee is going to be willing to continue through to the end of the process. I think. What am I missing?)
Hmm. That's not quite the right description of the illogic but something very odd is going on:
Suppose I find A and B incomparable and B and C incomparable but A is preferable to C.
Joe is willing to trade C=>B and B=>A.
I trade C into B knowing that I will eventually get A.
Then, I refuse to trade B to A!
But if Joe had not been willing to trade B=>A, I would not have traded C=>B!