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Could you or someone elaborate on that? It’s not obvious to me how uncertainty around K implies that equality is a good thing… it feels like there is some (perhaps obviously correct) assumption here on the distribution of K that’s missing here. Now if we say that utility provided to society by a person is concave with respect to their resources, then equality becomes obvious, but that seems different than this toy model (and also not obviously correct).

If the amount of resources is below Kpopulation - e.g. K/2population, wouldn’t that model suggest allocation K to half the population and 0 to the other half? If it is significantly above - e.g. 2Kpopulation, what’s the issue with giving everyone K and e.g. one person all the remaining resources?

One simple trick is doing a bijective transformation between your constrained input space and the unconstrained optimizer space. For example, if you have x>0 in your input space, you take the input from your optimizer and apply e^x to it. Or if you have a<x<b you can do a+b*logit(x). What exactly you choose will depend on your prior on how your function behaves.