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Jay_Schweikert comments on Zut Allais! - Less Wrong

23 Post author: Eliezer_Yudkowsky 20 January 2008 03:18AM

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Comment author: Jay_Schweikert 10 July 2011 08:52:32PM -1 points [-]

Maybe I'm missing something obvious, but doesn't diminishing marginal utility play a big role here? After all, almost all of us would prefer $1,000,000 with certainty to $2,000,100 with 50% probability, and it would be perfectly rational to do so -- not because of the "utility of certainty," but because $2 million isn't quite twice as good as $1 million (for most people). But if you offered us this same choice a thousand times, we would probably then take the $20,000,100, because the many coin flips would reduce the variance enough to create a higher expected utility, even with diminishing marginal returns. (If the math doesn't quite seem to work out, you could probably work out numbers that would.)

So it seems at least plausible that you could construct versions of the money pump problem where you could rationally prefer bid A to bid B in a one-off shot, but where you would then change your preference to bid B if offered multiple times. Obviously I'm not saying that's what's really going on -- Allais paradox surely does demonstrate a real and problematic inconsistency. But we shouldn't conclude from that it's always rational to just "shut up and multiply," at least when we're talking about anything other than "raw" utility.