Anyway, what if we try this one on for size: let’s say you are going to play a hand of Texas Hold ’em and you can choose one of the following three hands (none of them are suited): AK, JT, or 22. If we say that hand X > Y if hand X will win against hand Y more that 50% of the time, then AK > JT > 22 > AK > JT ….. etc. So in this case couldn’t one choose rationally and yet still be a “money pump”?
Hmmm.… I thought the point of your article at http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/ was that the difference between 1 and .99 was indeed much larger than, say, .48 and .49.
Anyway, what if we try this one on for size: let’s say you are going to play a hand of Texas Hold ’em and you can choose one of the following three hands (none of them are suited): AK, JT, or 22. If we say that hand X > Y if hand X will win against hand Y more that 50% of the time, then AK > JT > 22 > AK > JT ….. etc. So in this case couldn’t one choose rationally and yet still be a “money pump”?