Bounded utility functions still seem to cause problems when uncertainty is involved. For example, consider the aforementioned utility function U(n) = 1 - (1 / (n^2)), and let n equal the number of agents living good lives. Using this function, the utility of a 1 in 1 chance of there being 10 agents living good lives equals 1 - (1 / (10^2)) = 0.99, and the utility of a 9 in 10 chance of 3^^^3 agents living good lives and a 1 in 10 chance of no agents living good lives roughly equals 0.1 * 0 + 0.9 * 1 = 0.9. Thus, in this situation the agent would be willing to kill (3^^^3) - 10 agents in order to prevent a 0.1 chance of everyone dying, which doesn't seem right at all. You could modify the utility function, but I think this issue would still to exist to some extent.