This is not a mathematical tool that you can apply to the concepts you have in mind. Politics is multidimensional, and you do not even have the ability to quantify or measure the terms you are using.
Lest you think I'm talking through my hat, one of my professional areas of expertise was experimental design, and I developed systems of linear equations to predict the behavior of the combinations of ingredients that affect several properties of a product's behavior, using manipulation of matrices.
A human being is far more complex than you seem to perceive.
Please note my exercise was premised on the question as already framed, and I think the question of a measure of position on the political spectrum is left moot.
I will say that the beauty of statistics is that it will apply to whatever objective measure you care to devise, however you care to interpret it.