As a researcher doing data-stuff: there actually is a somewhat objective way to answer this! I don’t know the answer to the question itself though… and the method is quite boring

Usually how data scientists do this is to first collect a bunch of data… let’s say we have a 200~300 question comprehensive survey about ppl’s political beliefs. This survey would have a dimension of 200-300. We can include all of them but they would offer diminishing information (& is very confusing), so usually people trim it down to the most important dimensions only. We then apply dimensionality reduction/manifold method to reduce highly similar dimensions. I think in social sciences people call this factor analysis. Usually in my field people do PCA followed by UMAP, social scientists I think may do something differently but PCA is quite universal

Then researchers will be able to tell a few mathematically identified dimensions that contribute the most to the results. Say if the first dimension contributes 70% of the variation of people’s differences, and the second dimension another 25%… then we would have a 2-dimension model that can explain 95% of the differences and would be good enough. If the first dimension only 10%, second 8%… then a good model will need a lot more dimensions. This doesn’t tell what the dimensions are though, that’s up to the researchers to identify. If all of these work well, we’d have a simple, N-dimension model suggesting how people’s political beliefs are… and some of these might not map to what people would intuitively think of

Unless I’m mistaken, Big Five personality traits is developed this way for example… About politics, I found a 2013 research article that suggested two political dimensions: economic and social ideology

I guess this doesn’t quite answer the question… it just states how political dimensions (or any dimensions in data fields, really) came from, and the fact that there’s an old paper suggesting a two factor model of economic + social ideology. I don’t know how many dimensions are sufficient for politics, not to count for the fact that different countries/cultures treat this differently

People are inventing new terms constantly to politically differentiate themselves from the neighbour every time they disagree on any detail.

That compass could have as many dimensions as words and meanings are in a dictionary. It’s like every fucking thing must be perfectly categorised, distinguished and segregated.

How many do you want it to have.

The political compass is a tool to illustrate and compare political preferences. The more dimensions you add the more complicated it becomes.

After 3 it gets tricky to draw anything useful. You can still choose which political values to illustrate.

Here are some more options:

• Individualism vs collectivism
• Essentialism vs constructivism (are important traits of people fixed, or mutable?)
• Belief in conspiracy theories vs skepticism (people who believe one conspiracy theory usually believe many, also predicts mistrust in institutions like traditional media and scientists)

It’s worth thinking about whether dimensions like these are cause or effect, and political or personality traits. zlatiah points out that there are techniques for identifying which ones cause political behavior.

https://youtu.be/UuopBeaUN24

/s

I found a study that may be helpful.
The project is called the Chapel Hill Expert Survey, which is being conducted by Gary Marks of the University of North Carolina at Chapel Hill and others, and asks political experts in each country to evaluate the policy positions of major political parties in EU member states.

This survey interprets the multidimensional political conflict as stated in the question, and in the latest survey (Version 2025.1), it is measured by the following conflict terms:

Reference

Official

Project website

The 2024 Chapel Hill Expert Survey on political party positioning in Europe: Twenty-five years of party positional data - ScienceDirect

Unofficial

Introduction to the Chapel Hill Expert Survey – Blog d’Emilien Houard-Vial

経済・社会文化・グローバリゼーションー2020年の各国政党政治ー｜NIRA総合研究開発機構 (Article in Japanese)

politics is 1-dimensional thought. thats why its palatable to the lowest common denominators, its all based on FEAR and emotions.

One dimension:

Willingness to share Liberties with other people

Far Right = Ayn Rand

Far Left = some guy who just wants to live in a van down by the river and smoke weed all day

If we are trying to avoid losing any information due to abstraction, I’d say at least somewhere in the low hundreds.

All actions are done out of desire and human desires are numerous and often contradictory even in the same person. Many people who think they are utilitarian likely still wouldn’t be okay with the Omelas structure of torturing a single kid even if that act allowed thousands of others to live painless lives.

Is it more right to avoid violence altogether, or is violence to prevent the slaughter of others better than doing nothing?

Morality is complicated and since morality dictates much of how we interact with others, it is likely the most significant factor in politics.

The second most would be personal desires. People with weak or localized empathy don’t tend to care about any politics that doesn’t affect them or their desires directly. Since desires are also diverse, this is multidimensional too.

Now, that being said, if our goal is to reduce the dimensionality as much as possible… the answer is basically any number you want.

Data analysis techniques will let you reduce the dimensionality of n-dimensional data to whatever number you want. In fact using similar techniques to word embedding would likely be very effective even if you simply group people by how similar their views seem to be (no need for you to actually define dimensions)

If we assume that there are around as many important dimensions to politics as there are typical English words, then we can assume the number of dimensions needed for encoding a person’s politics without losing relationships would be about the same as a word embedding vector.

In typical LLMs this is anywhere from around 50-300 dimensions.

Honestly, now I’m really fucking curious. If you created a quiz with thousands of political/philosophical questions and then had a large enough number of people take the quiz, you could legitimately do this with an autoencoder and see how many hidden neurons (dimensions) you would need for a precise encoding.

You might not be able to tell what those dimensions represent, but it would be incredibly fascinating to be able to subtract political ideologies from one another like you can with word embeddings.

Like with good embeddings you can subtract “France” from “Paris” then add that to “Poland” and it will give you a vector very close to “Warsaw”

Imagine being able to map out political or philosophical ideologies like this! You could ask it how far away two ideologies are too, or ask it what the average between two ideologies is, etc.

I feel like that would be incredibly fascinating to mess around with AND like the average example it could give you an idea of gaps in our political spectrum, ideologies that don’t exist yet or haven’t been named. It could show you attractor points or clusters and give insight into inherent human nature.

Damn I want to make this.