Yeah, but left/right is a big part of what differentiates political parties. It's like the first factor in a PCA decomposition.

If you want to bring in rigorous analysis you have to first define what left/right even is. Is it economic policy? You really think the biggest thing that differentiates red/blue is economic policy? They both sit firmly on the right.

I would love to see a decent PCA decomposition if you've got one. The way Left/Right is defined seems pretty arbitrary and varies a lot between cultures.

It changes over time too. I learnt that it was about economic policy, but today it's some weird mixture of economic policy, progressive vs conservative, liberal vs totalitarian etc. For example, in the US right now it would be totally normal to label someone who doesn't support gay rights as "right wing". Left/right have essentially become buckets where certain arbitrary issues end up residing.