The following position seems fairly plausible to me. (1) Diminishing marginal utility is the only good strong reason for risk aversion; that is, the only thing that can justify a large difference between the value of $X and half the value of $2X. (2) But there are some good but weak reasons, which can’t produce a large difference—but if X is small then they may justify a fairly substantial relative difference. (3) Something a bit like actual human risk-averse behaviour can be justified by the combination of (1) when large sums are at stake and (2) when small sums are at stake.
(This is very strongly reminiscent of what happens with payday loan companies, which make small short-term loans with charges that are not very large in absolute terms but translate to absolutely horrifying numbers if you convert them to APRs; this isn’t only because payday lenders are evil sharks (though they might be) and payday loans are really high risk (though they might be) but also because some of the cost of lending money is more or less independent of the size and duration of the loan. If I lend you $100 for a day and charge $1 for the effort of keeping track of what I’m owed by whom and when, that’s an APR of over 3000%, but it’s not obviously unreasonable even so: most of that $1 isn’t really interest as such.)
The following position seems fairly plausible to me. (1) Diminishing marginal utility is the only good strong reason for risk aversion; that is, the only thing that can justify a large difference between the value of $X and half the value of $2X. (2) But there are some good but weak reasons, which can’t produce a large difference—but if X is small then they may justify a fairly substantial relative difference. (3) Something a bit like actual human risk-averse behaviour can be justified by the combination of (1) when large sums are at stake and (2) when small sums are at stake.
(This is very strongly reminiscent of what happens with payday loan companies, which make small short-term loans with charges that are not very large in absolute terms but translate to absolutely horrifying numbers if you convert them to APRs; this isn’t only because payday lenders are evil sharks (though they might be) and payday loans are really high risk (though they might be) but also because some of the cost of lending money is more or less independent of the size and duration of the loan. If I lend you $100 for a day and charge $1 for the effort of keeping track of what I’m owed by whom and when, that’s an APR of over 3000%, but it’s not obviously unreasonable even so: most of that $1 isn’t really interest as such.)