I see. Thank you Nick. I was confused by the idea that utility could be proportional. e.i. 100%*U[$1'000'000] = { 50%*U[$1'000'000] } * 2 because when you put 2 50%*U[$1'000'000] the utility was less than 100%*U[$1'000'000]. But that was because U[$1'000'000] = U[$1'000'000] is not always true depending on if it's the 1st or 2nd million. U[$1'000'000] going from $0 to $1'000'000 is not the same as U[$1'000'000] going from $1'000'000 to $2'000'000.

Back to Alais: * 1A. 100%*U[$24,000] + 0%*U[$0] * 1B. 33/34*U[$27,000] + 1/34*U[$0] * 2A. 34%*U[$24,000] + 66%*U[$0] * 2B. 33%*U[$27,000] + 67%*U[$0]

In 1A, U[$24,000] is going from $0 to $24,000. In 1A, U[$0] is going from $0 to $0. In 1B, U[$27,000] is going from $0 to $27,000. In 1B, U[$0] is going from $0 to $0. In 2A, U[$24,000] is going from $0 to $24,000. In 2A, U[$0] is going from $0 to $0. In 2B, U[$27,000] is going from $0 to $27,000. In 2B, U[$0] is going from $0 to $0. Looks like all the variables, U[money] = U[money] hold.

So if 1A > 1B then 100%*U[$24,000] + 0%*U[$0] > 33/34*U[$27,000] + 1/34*U[$0] - multiply by 34% 34%*( 100%*U[$24,000] + 0%*U[$0] ) > 34%*( 33/34*U[$27,000] + 1/34*U[$0] ) - add 66%*U[$0] (which makes the total percentages add up to 100%) 34%*( 100%*U[$24,000] + 0%*U[$0] ) + 66%*U[$0] > 34%*( 33/34*U[$27,000] + 1/34*U[$0] ) 66%*U[$0] - algebra 34%*U[$24,000] + 0%*U[$0] + 66%*U[$0] > 33%*U[$27,000] + 1%*U[$0] + 66%*U[$0] - more algebra 34%*U[$24,000] + 66%*U[$0] > 33%*U[$27,000] + 67%*U[$0] - meaning 2A > 2B if 1A > 1B

/sigh, all this time to rediscover the obvious.