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alyssavance 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.
No, it's not, and the problem asserted by Allais paradox is that the utility function is inconsistent, no matter what the risk preference.
I don't see anything in there that about how many times the choice has to happen, which is the very issue at stake.
If there's any unusualness, it's definitely on your side. When you buy a chocolate bar for a dollar, that "preference of a chocolate bar to a dollar" does not somehow mean that you are willing to trade every dollar you have for a chocolate bar, nor have you legally obligated yourself to redeem chocolate bars for dollars on demand (as a money pump would require), nor does anyone expect that you will trade the rest of your dollars this way.
It's called diminishing marginal utility. In fact, it's called marginal analysis in general.
It means you would trade B for A on the next opportunity to do so, not that you would indefinitely do it forever, as the money pump requires.
"When you buy a chocolate bar for a dollar, that "preference of a chocolate bar to a dollar" does not somehow mean that you are willing to trade every dollar you have for a chocolate bar, nor have you legally obligated yourself to redeem chocolate bars for dollars on demand (as a money pump would require), nor does anyone expect that you will trade the rest of your dollars this way."
Under normal circumstances, this is true, because the situation has changed after I bought the chocolate bar: I now have an additional chocolate bar, or (more likely) an additional bar's worth of chocolate in my stomach. My preferences change, because the situation has changed.
However, after you have bought A, and swapped A for B, and sold B, you have not gained anything (such as a chocolate bar, or a full stomach), and you have not lost anything (such as a dollar); you are in precisely the same position that you were before. Hence, consistency dictates that you should make the same decision as you did before. If, after buying the chocolate bar, it fell down a well, and another dollar was added to my bank account because of the chocolate bar insurance I bought, then yes, I should keep buying chocolate bars forever if I want to be consistent (assuming that there is no cost to my time, which there essentially isn't in this case).