Early on in my career, I worked in the New Product Introduction division, for a big US company that was very big on Six-sigma. Their idea of product design was very much like the OP : what is the best mathematical approach for a compromise. So say you want to design a new car, you will survey customers and come up with rankings of the desired qualities in a new model. (High/Medium/Low). You will assign 5 to High, 3 to Medium and 1 to Low
So lets pick 4 qualitiesL Inexpensiveness of the Car is of High importance (a 5 to customers), cost of maintenance is 1, Miles per gallon is a 3, Looks is a 5. (this becomes a sort of objective function)
Then you would take Design A, B, C… and say Design A has a low cost (5), is easy to maintain (5), MPG is poor 1 but looks is great (5)
So the score for Design A would be 5x5 +1x5+3x1+5x5 = 58
You would use this kind of design to narrow down the final design !!
Everything looks great on paper, but it did not work! That great company is in shambles now.
The problem is not the math but the inherent non-linearity of the system i.e. the value humans place on different aspects is not linear but maybe exponential. For the car case, for someone the cost maybe rated 100 points and looks maybe rated 2 points !!
This type of mathematical analysis also kills ingenuity / creativity and is very stifling for some people. Because the mathematics presupposes a domain of options and a range of resulting solutions. It presupposes for example that Angie knows what her “dream house” is, or Brian knows what his “dream hours are”.
For example : Replace Brain by Steve Jobs and Angie by Apple Customers. Now suppose they are trying to design the first iphone together …