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pengvado comments on The Absent-Minded Driver - Less Wrong
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I'm curious how you arrived at this. Shouldn't it be α = (1/2)p + (1 - p) = 1 - p/2? (The other implies that you are a thirder in the Sleeping Beauty Problem -- didn't Nick Bostrum have the last word on that one?) The payoff becomes α[p^2+4p(1-p)] + (1-α)[p+4(1-p)] = (1 - p/2)(4p - 3p^2) + (p/2)(4 - 3p) = 6p - (13/2)p^2 + (3/2)p^3, which has a (local) maximum around p = 0.577.
The conclusion remains the same, of course.
I'm a "who's offering the bet"er on Sleeping Beauty (which Bostrom has said is consistent with, though not identical to, his own model). And in this case I specified bets offered and paid separately at each intersection, which corresponds to the thirder conclusion.