Cardinal numbers for utilons?

I have a hunch.

Trying to add up utilons or hedons can quickly lead to all sorts of problems, which are probably already familiar to you. However, there are all sorts of wacky and wonderful branches of non-intuitive mathematics, which may prove of more use than elementary addition. I half-remember that regular math can be treated as part of set theory, and there are various branches of set theory which can have some, but not all, of the properties of regular math - for example, being able to say that X < Y, but not necessarily that X+Z > Y. A bit of Wikipedia digging has reminded me of Cardinal numbers, which seem at least a step in the right direction: If the elements of set X has a one-to-one correspondence with the elements of set Y, then they're equal, and if not, then they're not. This seems to be a closer approximation of utilons than the natural numbers, such as, say, if the elements of set X being the reasons that X is good.

But I could be wrong.

I'm already well past the part of math-stuff that I understand well; I'd need to do a good bit of reading just to get my feet back under me. Does anyone here, more mathematically-inclined than I, have a better intuition of why this approach may or may not be helpful?

(I'm asking because I'm considering throwing in someone who tries to follow a cardinal-utilon-based theory of ethics in something I'm writing, as a novel change from the more commonly-presented ethical theories. But to do that, I'd need to know at least a few of the consequences of this approach might end up being. Any help would be greatly appreciated.)