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DonGeddis comments on Allais Malaise - Less Wrong

20 Post author: Eliezer_Yudkowsky 21 January 2008 12:40AM

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Comment author: DonGeddis 21 January 2008 03:34:47PM 1 point [-]

Sorry for my typo in my example. Of course I meant to say that 3A was 100% at $24K, and 3B was 50%@$26K and 50%@22K. The whole point was for the math to come out with the same expected value at $24K, just 3B has more volatility. But I think everyone got my intent despite my typo.

Eliezer of course jumped right to the key, which is the (unrealistic) assumption of linear utility. I was going to log in this morning and suggest that the financial advice of "always get paid for accepting volatility" and/or "whenever you can reduce volatility while maintaining expected value, do so" was really a rule-of-thumb summary for common human utility functions. Which is basically what Eliezer suggested in the addendum, that log utility + Bayes results in the same financial advice.

The example I was going to try to suggest this morning, in investment theory, is diversification. If you invest in a single stock that historically returns 10% annually, but sometimes -20% and sometimes +40%, it is "better" to instead invest 1/10 of your assets in 10 such (uncorrelated) stocks. The expected return doesn't change: it's still 10% annually. But the volatility drops way down. You bunch up all the probability around the expected return (using a basket of stocks), whereas with a single stock the probabilities are far more spread out.

But probably you can get to this same conclusion with log utilities and Bayes.

My final example this morning was going to be on how you can use confidence to make further decisions, in between the time you accept the bet and the time you get the payoff. This is true, for example, for tech managers trying to get a software project out. It's far more important how _reliable_ the programmer's estimates are, than it is what their average productivity is. The overall business can only plan (marketing, sales, retail, etc) for the reliable parts, so the utility that the business sees from the volatile productivity is vastly lower.

But again, Eliezer anticipates my objection with his point #3 in the comments, about taking out a loan today and being confident that you can pay it back in five years.

My only final question, then, is: isn't "the opportunities to take advance preparations" sufficient to resolve the original Allais Paradox, even for the naive bettors who choose the "irrational" 1A/2B combination?