I'm not sure where you're getting the analogy of Buridan's Ass from "solvability of Galois groups." Solvability in radicals and picking between 2 (or however many) "equally good" choices feels like stretching. I also don't know where you're getting "the formula must output a single number." The solution to quadratics yields (at most) 2 numbers. The solution to cubics is big and nasty, yielding at most 3. And similarly for quartics, with at most 4. (I've only bothered with a few of these. You work in cases, the nastiest of which involves "reducing" the problem to a cubic.)

I see the analogy to "symmetry", but that's about it.

Now, solving the Buridan's Ass paradox is rather easy. Common Law just thinks it's cheating to point out that starving to death is less optimal than doing something other than starving to death. Or it's a bias. Or something.