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alethiophile comments on Zut Allais! - Less Wrong

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

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Comment author: alethiophile 14 December 2010 05:06:05AM -1 points [-]

I think there are some places where it is rational to take this kind of bet the less-expected-value way for a greater probability. Say you're walking along the street in tears because mobsters are going to burn down your house and kill your family if you don't pay back the $20,000 you owe them and you don't have the cash. Then some random billionaire comes along and offers you either A. $25,000 with probability 1 or B. $75,000 with probability 50%. By naive multiplication, you should take the second bet, but here there's a high additional cost of failure which you might well want to avoid with high probability. (It becomes a decision about the utilities of not paying the mob vs. having X additional money to send your kid to college afterwards. This has its own tipping point; but there's a rational case to be made for taking A over B.)

Comment author: shokwave 14 December 2010 06:02:05AM 1 point [-]

This is why you should use expected utility calculations. The utility of $20,000 also contains the utility of saving your family's lives (say $1,650,000) and retaining a house ($300,000), so choosing between 100% chance of $1,975,000 or 50% chance of $2,025,000 is much easier.