Utility is approximately the logarithm of money. Pretend otherwise, and you will get results that go against the intuition, duh.
To be clearer, utility is approximately the logarithm of your wealth, not of the change to your wealth. So there’s a hidden number lurking in each of those questions—if you have $100k (5) of wealth, then option A brings it up to $100240 (5.00104) and option B brings it up to either $101000 (5.00432) with 25% probability and leaves it where it is with 75% probability, which works out to a weighted average log wealth of 5.00108, which is higher, so go with B.
But if your wealth is $1k (3), then option A brings you up to a weighted average of 3.09 and B brings you up to a weighted average of 3.07. So go with A!
(The breakeven point for this particular option is a starting wealth of $8800.)
To be clearer, utility is approximately the logarithm of your wealth, not of the change to your wealth. So there’s a hidden number lurking in each of those questions—if you have $100k (5) of wealth, then option A brings it up to $100240 (5.00104) and option B brings it up to either $101000 (5.00432) with 25% probability and leaves it where it is with 75% probability, which works out to a weighted average log wealth of 5.00108, which is higher, so go with B.
But if your wealth is $1k (3), then option A brings you up to a weighted average of 3.09 and B brings you up to a weighted average of 3.07. So go with A!
(The breakeven point for this particular option is a starting wealth of $8800.)
I am confused. Pick B every time? Even although the weighted average of A is better in the second case? That’s supposed to be “So go with A!” right?
Typo fixed; thanks!