But ultimately to make a bet at even odds all Mitchell needs is to be confident that if someone takes him up on the bet then he has 50% or more chance of being correct. The size of the bet only matters indirectly as an incentive for others to do more research before betting.
This would only be true if money had linear utility value [1]. I, for example, would not take a $1000 bet at even odds even if I had 75% confidence of winning, because with my present financial status I just can’t afford to lose $1000. But I would take such a bet of $100.
The utility of winning $1000 is not the negative of the utility of losing $1000.
[1] or, to be precise, if it were approximately linear in the range of current net assets +/- $1000
This would only be true if money had linear utility value [1]. I, for example, would not take a $1000 bet at even odds even if I had 75% confidence of winning, because with my present financial status I just can’t afford to lose $1000. But I would take such a bet of $100.
The utility of winning $1000 is not the negative of the utility of losing $1000.
[1] or, to be precise, if it were approximately linear in the range of current net assets +/- $1000
From what I have inferred about Michael’s financial status the approximation seemed safe enough.
Fair enough in this case, but it’s important to avoid assuming that the approximation is universally applicable.