actually... I don't agree with this example as being a good example of intuition failing. the problem is people think about this scenario as if it were real life. in real life there would be a delayed payout. in the case of a delayed payout on their "ticket" the ticket with 100% certainty is more LIQUID than the ticket with the better expectation. liquidity itself has utility. maybe the liquidity of the certain payoff is only due to the rest of society being dumb; however even if that is the case if you know the rest of society is dumb you must take that into account when making your decision. in this case the brain does not seem to be wrong and seems to actually be choosing correctly. the brain is just taking your example and adding lots of extra details to it to make it feel more realistic (this is certainly an undesired effect for researchers trying to learn about people's thoughts or interests but who cares about them). the brain often adds a bunch of assumed details to a confusing situation, this is basically the definition of how intuition works. now, you have to consider the odds of this exact example coming up or the odds of the imagined example coming up... and how well the brain will likely handle each situation... then use that information to determine if the brain is actually mistaken or not.

in the case of electronic store warranties they usually aren't worthwhile because they are designed to not be worthwhile. just like mail-in rebates are designed to often go unredeemed... however in the case where your personal time is more valuable by far than any of the costs, it starts to make sense.

on another note how rich did feynmann or kac get? (either a ton, or not that much depending on if they wanted to help people or take their pennies!)

Allais Malaise

by Eliezer Yudkowsky 1 min read21st Jan 200838 comments


Continuation ofThe Allais Paradox, Zut Allais!

Judging by the comments on Zut Allais, I failed to emphasize the points that needed emphasis.

The problem with the Allais Paradox is the incoherent pattern 1A > 1B, 2B > 2A.  If you need $24,000 for a lifesaving operation and an extra $3,000 won't help that much, then you choose 1A > 1B and 2A > 2B.  If you have a million dollars in the bank account and your utility curve doesn't change much with an extra $25,000 or so, then you should choose 1B > 1A and 2B > 2A.  Neither the individual choice 1A > 1B, nor the individual choice 2B > 2A, are of themselves irrational.  It's the combination that's the problem.

Expected utility is not expected dollars.  In the case above, the utility-distance from $24,000 to $27,000 is a tiny fraction of the distance from $21,000 to $24,000.  So, as stated, you should choose 1A > 1B and 2A > 2B, a quite coherent combination.  The Allais Paradox has nothing to do with believing that every added dollar is equally useful.  That idea has been rejected since the dawn of decision theory.

If satisfying your intuitions is more important to you than money, do whatever the heck you want.  Drop the money over Niagara falls.  Blow it all on expensive champagne.  Set fire to your hair.  Whatever.  If the largest utility you care about is the utility of feeling good about your decision, then any decision that feels good is the right one.  If you say that different trajectories to the same outcome "matter emotionally", then you're attaching an inherent utility to conforming to the brain's native method of optimization, whether or not it actually optimizes.  Heck, running around in circles from preference reversals could feel really good too.  But if you care enough about the stakes that winning is more important than your brain's good feelings about an intuition-conforming strategy, then use decision theory.

If you suppose the problem is different from the one presented - that the gambles are untrustworthy and that, after this mistrust is taken into account, the payoff probabilities are not as described - then, obviously, you can make the answer anything you want.

Let's say you're dying of thirst, you only have $1.00, and you have to choose between a vending machine that dispenses a drink with certainty for $0.90, versus spending $0.75 on a vending machine that dispenses a drink with 99% probability.  Here, the 1% chance of dying is worth more to you than $0.15, so you would pay the extra fifteen cents.  You would also pay the extra fifteen cents if the two vending machines dispensed drinks with 75% probability and 74% probability respectively.  The 1% probability is worth the same amount whether or not it's the last increment towards certainty.  This pattern of decisions is perfectly coherent.  Don't confuse being rational with being shortsighted or greedy.

Added:  A 50% probability of $30K and a 50% probability of $20K, is not the same as a 50% probability of $26K and a 50% probability of $24K.  If your utility is logarithmic in money (the standard assumption) then you will definitely prefer the latter to the former:  0.5 log(30) + 0.5 log(20)  <  0.5 log(26) + 0.5 log(24).  You take the expectation of the utility of the money, not the utility of the expectation of the money.