Unfortunately it also introduces a ton of new ones, because while it's easy to compare ordinal preferences, there's no single good intuitive way to compare cardinal preferences.
If you give voters a scale from 0 to 10, one person's 3 is another person's 5. It's not even remotely clear that one person's vote of 8 should count the same as two other people's vote of 4, or even that the same person's 8 should count double their 4. Is the preferences scale linear? Logarithmic? Exponential? Other?
The arbitrariness and therefore unknown meaning of cardinal voting scores, and cardinal preferences generally, is the reason why philosophers mainly abandoned cardinal measures of utility a long time ago, and most utilitarian philosophy is based on knowledge of ordinal preferences only.
What? You can literally rank them if you're confused. Better yet, rank them with unequal spacing (A:5, B:4, C:2).
It is hard to take your claim seriously because it has been tested in real world settings. This isn't a theoretical proposition (and you're arguing over theory). Also did you really just say "logarithmic vs exponential?"
The reality doesn't match your hypothesis and that is testable.
You're claiming philosophers abandoned it and I don't see evidence for this. Also I'm not sure why philosophers matter here, this isn't philosophy. Cardinal methods are the preference of most researchers that study voting. I don't know about you, but I tend to go with expert opinion (not absolutely, but it is a strong signal that something is the right path to follow. Then you just vet the work).
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.
> Again, the fundamental problem with cardinal voting is simply that there's no intuitive, easily agreed-upon meaning for what cardinal values even mean.
Cardinal values are perfectly meaningful. They can be interpreted as expressions of ordinal preference for probabilities of different outcomes, for instance.
https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster...
For example, if I prefer Strawberry ice cream over Chocolate ice cream, and Chocolate ice cream over Garlic ice cream, and am given the choice between:
- A box that definitely contains Chocolate - A box that has a 50/50 chance of containing Strawberry or Garlic
I would choose the safe bet of Chocolate, because my preference for C>G is much stronger than my preference for S>C. By varying the probability and making the choice again, we can estimate the ratio of the strengths of my preferences between the three options.
You're right, passion matters.