GreedyAlgorithm comments on Principles of Disagreement - Less Wrong
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If they're both about equally likely to reason as well, I'd say Eliezer's portion should be p*$20, where ln(p/(1-p))=(1.0*ln(0.2/0.8)+1.0*ln(0.85/0.15))/(1.0+1.0)=0.174 ==> p=0.543. That's $10.87, and he owes NB merely fifty-six cents.
Amusingly, if it's mere coincidence that the actual split was 3:4 and in fact they split according to this scheme, then the implication is that we are trusting Eliezer's estimate 86.4% as much as NB's.