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Psychohistorian comments on Expected utility without the independence axiom - Less Wrong
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"1) I wasn't claiming that Allais is about risk aversion."
The difference between your preferences over choosing lottery A vs. lottery B when both are performed a million times, and your preferences over choosing A vs. B when both are performed once, is a measurement of your risk aversion; this is what Gray Area was talking about, is it not?
"Believe it or not, when I say, "I prefer B to A", it doesn't mean "I hereby legally obligate myself to redeem on demand any B for an A""
Then you must be using a different (and, I might add, quite unusual) definition of the word "preference". To quote dictionary.com:
pre⋅fer /prɪˈfɜr/ [pri-fur] –verb (used with object), -ferred, -fer⋅ring. 1. to set or hold before or above other persons or things in estimation; like better; choose rather than: to prefer beef to chicken.
What does it mean to say that you prefer B to A, if you wouldn't trade B for A if the trade is offered? Could I say that I prefer torture to candy, even if I always choose candy when the choice is offered to me?
Typo: Did you mean "prefer A to B"?
I prefer B to A does not imply I prefer 10B to 10A, or even I prefer 2B to 2A. Expected utility != expected return.
I agree pretty much completely with Silas. If you want to prove that people are money pumps, you need to actually get a random sample of people and then actually pump money out of them. You can't just take a single-shot hypothetical and extrapolate to other hypotheticals when the whole issue is how people deal with the variability of returns.
Strictly speaking, Eliezer's formulation of the Allais Paradox is not the one that has been experimentally tested. I believe a similar money pump can be implemented for the canonical version, however -- and Zut Allais! shows that people can be turned into money pumps in other situations.
"I prefer B to A does not imply I prefer 10B to 10A, or even I prefer 2B to 2A. Expected utility != expected return."
Of course, but, as I've said (I think?) five times now, you never actually get 2B or 2A at any point during the money-pumping process. You go from A, to B, to nothing, to A, to B... etc.
For examples of Vegas gamblers actually having money pumped out of them, see The Construction of Preference by Sarah Lichtenstein and Paul Slovic.