James_Ernest comments on Solve Psy-Kosh's non-anthropic problem - Less Wrong
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The expected value is $1000 (10 * p - 10 p^ 10). Maximums and minimums of functions may occur when the derivative is zero, or at boundaries.
The derivative is $1000(10 - 100 p^ 9). This is zero when p = 0.1^(1/9) ~= 0.774. The boundaries of 0 and 1 are minima, and this is a maximum.
EDIT: Huh. This simple calculation that mildly adds to the parent is worth more karma than the parent? I thought the parent really got to the heart of things with: "(because there's no reliable way to account for the decisions of others if they depend on yours)" Of course, TDT and UDT are attempts to do just that in some circumstances.
Shouldn't the expected value be $1000 (10p)*(1-p^10) or $1000 (10p - 10p^11) ? (p now maximised at 0.7868... giving EV $7.15K)
That does look right.