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gjm comments on Omega's Idiot Brother, Epsilon - Less Wrong Discussion
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Comments (7)
Your returns must be very rapidly diminishing. If u is your kilobucks-to-utilons function then you need [7920u(1001)+80u(1)]/8000 > [3996u(1000)+4u(0)]/4000, or more simply 990u(1001)+10u(1) > 999u(1000)+u(0). If, e.g., u(x) = log(1+x) (a plausible rate of decrease, assuming your initial net worth is close to zero) then what you need is 6847.6 > 6901.8, which doesn't hold. Even if u(x) = log(1+log(1+x)) the condition doesn't hold.
If we fix our origin by saying that u(0)=0 (i.e., we're looking at utility change as a result of the transaction) and suppose that at any rate u(1001) <= 1001/1000.u(1000), which is certainly true if returns are always diminishing, then "two-boxing is better because of diminishing returns" implies 10u(1) > 8.01u(1000). In other words, gaining $1M has to be no more than about 25% better than gaining $1k.
Are you sure you two-box because of diminishing returns?
Interesting. My thought process was that it's worth losing $8000 in EV to avoid a 1% chance of losing $1000. I think my original statement was true, but perhaps poorly calibrated; these days I shouldn't be that risk-averse.