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alyssavance comments on Expected utility without the independence axiom - Less Wrong
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"What, are they fake tickets that can't actually be used now?"
No, they're just the same tickets. There's only ever one of each. If I sell you a chocolate bar, trade the chocolate bar for a bag of Skittles, buy the bag of Skittles, and repeat ten thousand times, this does not mean I have ten thousand of each; I'm just re-using the same ones.
"They might, but you would have to actually test it out. They don't become irrational until such a thing actually happens."
We did test it out, and yes, people did act as money pumps. See The Construction of Preference by Sarah Lichtenstein and Paul Slovic.
You can also listen to an interview with one of Sarah Lichtenstein's subjects who refused to make his preferences consistent even after the money-pump aspect was explained:
http://www.decisionresearch.org/publications/books/construction-preference/listen.html
That is an incredible interview.
Admitting that the set of preferences is inconsistent, but refusing to fix it is not so bad a conclusion - maybe he'd just make it worse (eg, by raising the bid on B to 550). At times he seems to admit that the overall pattern is irrational ("It shows my reasoning process isn't too good"). At other times, he doesn't admit the problem, but I think you're too harsh on him in framing it as refusal.
I may be misunderstanding, but he seems to say that the game doesn't allow him to bid higher than 400 on B. If he values B higher than 400 (yes, an absurd mistake), but sells it for 401, merely because he wasn't allowed to value it higher, then that seems to me to be the biggest mistake. It fits the book's title, though.
Maybe he just means that his sense of math is that the cap should be 400, which would be the lone example of math helping him. He seems torn between authority figures, the "rationality" of non-circular preferences and the unnamed math of expected values. I'm somewhat surprised that he doesn't see them as the same oracle. Maybe he was scarred by childhood math teachers, and a lone psychologist can't match that intimidation?
That sounds to me as though he is using expected utility to come up with his numbers, but doesn't understand expected utility, so when asked which he prefers he uses some other emotional system.