You have a person whose utility is U = Square root of I. They have two choices: A. Vote for action B. Vote against action. If they choose B. They get $5 Million. If they choose A. they have a 30% chance of making $80 million and 70% chance of making $1 million. So far so good.
But if they make the $80 million, there is a possibility they will loose $10 million of it. The problem is what's the maximum probability of that last last thing happening (-$10 million) that will induce the person to vote for action?
So, the way I did it was just EU(sr $5million) = .7EU(sr $1million) + .3EU(sr $80million) - p(sr $10mill). Where "sr" square root. That gave me a max of 36% probability.
*What I'm confused about is that there is only a 30% chance of facing the probability of -$10,000 so it doesn't seem like it should receive the same weight as the $80mill and $1mill ? Its like a chance of a chance. But when I did .3 * p(sr $10million) it gave me a probably greater than 100% which I know was wrong.