This sounds like the sort of thing I reply to in these two paragraphs?
I suppose one thing you could do here is pretend you can fit infinite rounds of the game into a finite time. Then Linda has a choice to make: she can either maximize expected wealth at tn for all finite n, or she can maximize expected wealth at tω, the timestep immediately after all finite timesteps. We can wave our hands a lot and say that making her own bets would do the former and making Logan’s bets would do the latter, though I don’t endorse the way we’re treating infinties here.
Even then, I think what we’re saying is that Linda is underspecified. Suppose she’s offered a loan, “I’ll give you £1 now and you give me £2 in a week”. Will she accept? I can imagine a Linda who’d accept and a Linda who’d reject, both of whom would still be expected-money maximizers, just taking the expectation at different times and/or expanding “money” to include debts. So you could imagine a Linda who makes short-term sacrifices in her expected-money in exchange for long-term gains, and (again, waving your hands harder than doctors recommend) you could imagine her taking Logan’s bets. But this is more about delayed gratification than about Logan’s utility function being better for Linda than her own, or anything like that.
I might be wrong about how you think Sarah’s post relates to mine. But if you think it brings up something that contradicts my post, or that my post ought to respond to but doesn’t, or something like that, are you able to point at it more specifically?
This sounds like the sort of thing I reply to in these two paragraphs?
I might be wrong about how you think Sarah’s post relates to mine. But if you think it brings up something that contradicts my post, or that my post ought to respond to but doesn’t, or something like that, are you able to point at it more specifically?