On Mathematical Applications in the 3-Axis Political Model

The information in this webpage should be taken with a grain of salt.

The context required to understand this comes from my previous “On the 3-Axis Political Model.”

An issue in politics and political discourse is comparison. People on social media and elsewhere will casually call something similar (or exactly like) another belief. Common ones are comparing Bernie Sanders to the Soviet Union, Donald Trump to Hitler, and Joe Biden to China.

Each of these comparisons are ridiculous, of course, so it may seem that there should be a way to truly compare how alike two political things are. Thankfully, with my 3-axis model, this becomes possible.

A 3-Axis Political Model with Coordinates

Above is shown a modified version of my 3-axis model diagram to include numbers for each point on the scale. The numbers allow one to define where upon these axes they lie, with benefit added from the subdivisions.

So how, exactly, does this work? First, one must define what they want to compare. Then, they find each entities’ position on these three axes. Let Entity 1 be (X1, Y1, Z1) and Entity 2 be (X2, Y2, Z2).

Then, the math. We first plug those coordinates in the three-dimensional distance formula, such as with a calculator. We then plug that distance into the x value of the equation
y = -4.50835x + 100 and solve for y, such as with Wolfram|Alpha. For ease of use, round this number to the nearest integer.

This is not the easiest thing to do, so I have created a calculator below to automate the process.

X10
Y10
Z10
X20
Y20
Z20

Your result will be here!

So, after all this math, how correct are the comparisons? Below, the numbers are both shown and ran. (Keep in mind that the results shouldn’t be taken too seriously. I’m no political science PHD.)


Bernie Sanders is defined as (-1,-1,-3)

Soviet Union is defined as (7,-5,5)

Bernie Sanders is 46% like the Soviet Union.


Donald Trump is defined as (3,2,3)

Hitler is defined as (7,1,7)

Donald Trump is 74% like Hitler.


Joe Biden is defined as (2,1,-1)

China is defined as (7,-4,7)

Joe Biden is 52% like China.


This webpage was originally published 25 November 2020 and was last modified 26 February 2021.