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
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