The popular assumption is that a political ideal is represented by the center of mass of the people who claim to subscribe to it.

That would make the theory untestable. It would only be pollable, and the representation would be in continual drift.

Real ideals are testable and have some unchanging basis which can be validated or invalidated.

This is how math, engineering, science, technology and all the things that are widely known for actually working work.

I am currently in the process of testing for an exam, so I am constantly reminded of exactly what the testing and validation process is. The exam pertains to a computer system, AWS, so I can log in and validate or invalidate any of the questions I have placed a bet on with an answer in the exam.