dlthomas comments on Morality is not about willpower - Less Wrong

9 Post author: PhilGoetz 08 October 2011 01:33AM

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Comment author: dlthomas 21 October 2011 07:57:03PM *  1 point [-]

I don't have the time to examine the paper in depth just now (I certainly will later, it looks interesting) but it appears our proximate disagreement is over what you meant when you said "risk aversion" - I was taking it to mean a broader "demanding a premium to accept risk", whereas you seem to have meant a deeper "the magnitudes of risk aversion we actually observe in people for various scenarios." Assuming the paper supports you (and I see no reason to think otherwise), then my original objection does not apply to what you were saying.

I am still not sure I agree with you, however. It has been shown that, hedonically, people react much more strongly to loss than to gain. If taking a loss feels worse than making a gain feels good, then I might be maximizing my expected utility by avoiding situations where I have a memory of taking a loss over and above what might be anticipated looking only at a "dollars-to-utility" approximation of my actual utility function.

Comment author: taw 22 October 2011 01:06:49AM 3 points [-]

I was taking it to mean a broader "demanding a premium to accept risk"

The only reason expected utility framework seems to "work" for single two-outcome bets is that is has more parameters to tweak than datapoints we want to simulate, and we throw away utility curve immediately other than for 3 points - no bet, bet fail, bet win.

If you try to reuse this utility curve for any other bet or bet with more than two outcomes, you'll start seeing the same person accepting infinite, near-zero, or even negative risk premia.

Comment author: dlthomas 26 October 2011 05:22:37PM 1 point [-]

Could you provide a simple (or at least, near minimally complex) example?

Comment author: taw 29 October 2011 06:22:30AM 0 points [-]

Suppose that, from any initial wealth level, a person turns down gambles where she loses $100 or gains $110, each with 50% probability. Then she will turn down 50-50 bets of losing $1,000 or gaining any sum of money.

A person who would always turn down 50-50 lose $1,000/gain $1,050 bets would always turn down 50-50 bets of losing $20,000 or gaining any sum. These are implausible degrees of risk aversion.

Suppose we knew a risk-averse person turns down 50-50 lose $100/gain $105 bets for any lifetime wealth level less than $350,000, but knew nothing about the degree of her risk aversion for wealth levels above $350,000. Then we know that from an initial wealth level of $340,000 the person will turn down a 50-50 bet of losing $4,000 and gaining $635,670

Examples in paper are very simple (but explaining them with math and proving why expected utility fails so miserably takes much of the paper).

The intuition for such examples, and for the theorem itself, is that within the expected-utility framework turning down a modest-stakes gamble means that the marginal utility of money must diminish very quickly for small changes in wealth.

Comment author: dlthomas 29 October 2011 08:05:07PM 0 points [-]

You are being frustrating.

Your citations here are talking about trying to model human behavior based on trying to fit concave functions of networth-to-utility to realistic numbers. The bit you quoted here was from a passage wherein I was ceding this precise point.

I was explaining that I had previously thought you to be making a broader theoretical point, about any sort of risk premia - not just those that actually model real human behavior. Your quoting of that passage lead me to believe that was the case, but your response here leads me to wonder whether there is still confusion.

If you try to reuse this utility curve for any other bet or bet with more than two outcomes, you'll start seeing the same person accepting infinite, near-zero, or even negative risk premia.

Do you mean this to apply to any theoretical utility-to-dollars function, even those that do not well model people?

If so, can you please give an example of infinite or negative risk premia for an agent (an AI, say) whose dollars-to-utility function is U(x) = x / log(x + 10).

Comment author: taw 30 October 2011 09:37:16PM 0 points [-]

This utility function has near zero risk aversion at relevant range.

Assuming our AI has wealth level of $10000, it will happily take a 50:50 bet of gaining $100.10 vs losing $100.00.

It also gets to infinities if there's a risk of dollar worth below -$10.

Comment author: dlthomas 30 October 2011 10:24:35PM 0 points [-]

This utility function has near zero risk aversion at relevant range.

Assuming our AI has wealth level of $10000, it will happily take a 50:50 bet of gaining $100.10 vs losing $100.00.

Yes, it is weak risk aversion - but is it not still risk aversion, as I had initially meant (and initially thought you to mean)?

It also gets to infinities if there's a risk of dollar worth below -$10.

Yes, of course. I'd considered this irrelevant for reasons I can't quite recall, but it is trivially fixed; is there a problem with U(x) = x/log(x+10)?

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