I didn’t believe that claim, so I looked at the paper. The key piece is that you must always turn down the 50⁄50 lose 10/gain 10.10 bet, no matter how much wealth you have—i.e. even if you had millions or billions of dollars, you’d still turn down the small bet. Considering that assumption, I think the real-world applicability is somewhat more limited than the paper’s abstract seems to indicate.
That said, there are multiple independent lines of evidence in various contexts suggesting that humans’ degree of risk-aversion is too strong to be accounted for by diminishing marginals alone, so I do still think that’s true.
The paper has some more sophisticated examples that make less stringent assumptions. Here are a couple. “Suppose, for instance, we know a risk-averse person turns down 50-50 lose $100/gain $105 bets for any lifetime wealth level less than (say) $350,000, but know nothing about her utility function for wealth levels above $350,000, except that it is not convex. 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. If we only know that a person turns down lose $100/gain $125 bets when her lifetime wealth is below $100,000, we also know she will turn down a 50-50 lose $600/gain $36 billion bet beginning from a lifetime wealth of $90,000.”
Bets have fixed costs to them in addition to the change in utility from the money gained or lost. The smaller the bet, the more those fixed costs dominate. And at some point, even the hassle from just trying to figure out that the bet is a good deal dwarfs the gain in utility from the bet. You may be better off arbitrarily refusing to take all bets below a certain threshhold because you gain from not having overhead. Even if you lose out on some good bets by having such a policy, you also spend less overhead on bad bets, which makes up for that loss.
The fixed costs also change arbitrarily; if I have to go to the ATM to get more money because I lost a $10.00 bet, the disutility from that is probably going to dwarf any utility I get from a $0.10 profit, but whether the ATM trip is necessary is essentially random.
Of course you could model those fixed costs as a reduction in utility, in which case the utility function is indeed no longer logarithmic, but you need to be very careful about what conclusions you draw from that. For instance, you can’t exploit such fixed costs to money pump someone.
Yup, I agree with all that, and I think it is one of the reasons for (at least some instances of) loss aversion. I wonder whether there have been attempts to probe loss aversion in ways that get around this issue, maybe by asking subjects to compare scenarios that somehow both have the same overheads
I didn’t believe that claim, so I looked at the paper. The key piece is that you must always turn down the 50⁄50 lose 10/gain 10.10 bet, no matter how much wealth you have—i.e. even if you had millions or billions of dollars, you’d still turn down the small bet. Considering that assumption, I think the real-world applicability is somewhat more limited than the paper’s abstract seems to indicate.
That said, there are multiple independent lines of evidence in various contexts suggesting that humans’ degree of risk-aversion is too strong to be accounted for by diminishing marginals alone, so I do still think that’s true.
The paper has some more sophisticated examples that make less stringent assumptions. Here are a couple. “Suppose, for instance, we know a risk-averse person turns down 50-50 lose $100/gain $105 bets for any lifetime wealth level less than (say) $350,000, but know nothing about her utility function for wealth levels above $350,000, except that it is not convex. 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. If we only know that a person turns down lose $100/gain $125 bets when her lifetime wealth is below $100,000, we also know she will turn down a 50-50 lose $600/gain $36 billion bet beginning from a lifetime wealth of $90,000.”
Bets have fixed costs to them in addition to the change in utility from the money gained or lost. The smaller the bet, the more those fixed costs dominate. And at some point, even the hassle from just trying to figure out that the bet is a good deal dwarfs the gain in utility from the bet. You may be better off arbitrarily refusing to take all bets below a certain threshhold because you gain from not having overhead. Even if you lose out on some good bets by having such a policy, you also spend less overhead on bad bets, which makes up for that loss.
The fixed costs also change arbitrarily; if I have to go to the ATM to get more money because I lost a $10.00 bet, the disutility from that is probably going to dwarf any utility I get from a $0.10 profit, but whether the ATM trip is necessary is essentially random.
Of course you could model those fixed costs as a reduction in utility, in which case the utility function is indeed no longer logarithmic, but you need to be very careful about what conclusions you draw from that. For instance, you can’t exploit such fixed costs to money pump someone.
Yup, I agree with all that, and I think it is one of the reasons for (at least some instances of) loss aversion. I wonder whether there have been attempts to probe loss aversion in ways that get around this issue, maybe by asking subjects to compare scenarios that somehow both have the same overheads