I really know nothing about this sort of thing so hopefully I can at least articulate what I'm trying to find out.
Let's say there's five qualities that can be represented numerically, and these qualities work in harmony; thus one set of numbers can be considered "better" than another set.
If we were given the knowledge for example that {1,2,6,3} is a "better" set of numbers than both {2,1,6,7} and {5,5,1,2} but not better than {4,5,2,1} or {3,6,7,3}, how might we go about estimating the optimal set of numbers?
Note that in reality there would be thousands of comparisons of sets to work from (I doubt any meaningful estimate could be arrived at from just the five above).
(Also, the actual numbers wouldn't necessarily be discrete like in my examples).
Edit: For context, I'm curious about making an evaluation function of a chess board. The various qualities would be things like the number of isolated pawns, in how many ways the opposing player can give check, things like that. But these need to be weighted by multiplying by a constant, because obviously some factors are more important than others. So if I have the AI play itself with one side having constants {a_1, a_2, a_3, a_4, ...} and the other side having constants {b_1, b_2, b_3, b_4, ...} then the winning side's constants will be deemed to be better than the losing side's. If I do this thousands of times then I'll hopefully be able to estimate the ideal values for these constants.