Sure --- there's a neat paper by Franssen (2006) that demonstrates the formal equivalence between optimization problems and the social policy problems Arrow was concerned with. Basically, Arrow says that some constituents will always lose out under any social policy. Franssen showed that you can swap out "composite cost metric" for social policy and "components of the cost metric" for constituents, and the same arguments apply.

I didn't mean to say that it wasn't possible, you probably don't need a subjective measure of quality. I think you could empirically discover some objective characteristics of good chalk that would do the trick. You could at least quickly reject the worst chalk which is too brittle and too hard. I meant to say that there was and is no way that is recognized sufficiently universally that enables one to specify a chalk with the desirable properties to a gov't purchasing agent such that s/he can buy the right stuff.