If you have a problem with dichotomous outcomes, you can turn the outcome into a continuum to see if that helps solve the issue.
For example, imagine you are trying to decide which individuals in a population should get a vaccine in order to provide best overall immunity in the community. It’s a binary outcome but you can make the outcome continuous and just split in half (everyone above 50% probability gets the vaccine). Such a relaxation requires at worst twice as many vaccine doses, but is much easier to solve.