> What? You can literally rank them if you're confused.

That's ordinal, not cardinal then. Your example "(A:5, B:4, C:2)" gives zero indication as to what 5 vs 4 means, or 4 vs 2, beyond simply being "greater than". That's the entire point.

> It is hard to take your claim seriously because it has been tested in real world settings.

I have no idea what that even means. Any voting system can be "tested". It doesn't mean it produces desirable results. The philosophies behind different voting methods aren't "testable". Political philosophy is philosophy because it isn't testable -- it's about what's desirable from some ethical viewpoint. E.g. we don't "test" majoritarian voting, we defend it from principles of equality.

> Also did you really just say "logarithmic vs exponential?"

Yes I did. y=2^x and y=log(x) have different shapes qualitatively. In other words, is voting 10 twice as strong as voting for 9, or only a teensy bit stronger? Not sure what's confusing you here, or what words you think would express that difference more clearly.

> You're claiming philosophers abandoned it and I don't see evidence for this.

It's just the basic history of utilitarianism or consequentialism. Any survey on that can point you in the right direction as to why cardinal preference have been largely abandoned.

(I'm obviously not talking about economics where "utility" is commonly measured in dollars. Most analyses of voting methods are concerned with what should be the "right" outcome, not the dollar-maximizing outcome. Social choice theory has been the attempt by economists to essentially measure votes in dollars, but even that still works almost entirely with ordinal preferences that are then analyzed in dollar outcomes.)

> Also I'm not sure why philosophers matter here, this isn't philosophy.

Voting methods are a huge part of political philosophy. Of course it is. It basically straddles political philosophy and political science in the literature. (Then there are some additional contributions by economists, especially when it gets deeper into the mathematics of it, mainly in social choice theory.)

> Cardinal methods are the preference of most researchers that study voting.

That's absolutely the opposite of my experience and knowledge. There are absolutely some people who study them, but they're absolutely not the focus of "most" researchers, at least not in the realm of political philosophy and political science. Voting with cardinal preferences is also barely used in real-world political governance.

Again, the fundamental problem with cardinal voting is simply that there's no intuitive, easily agreed-upon meaning for what cardinal values even mean. Most succinctly: on a 10-point scale, define the difference between a "4" and a "5", and argue why your definition is superior to 10 other definitions that are trivial to come up with. Also explain how you'll get voters to reliably understand and vote according to that same definition as well.

On the other hand, ordinal preferences are entirely intuitive and unambiguous to express and interpret. Which isn't to say they're perfect, but they give researchers something they can actually work with, both theoretically and practically.