Non sequitor. In a high dimensional space, things varying greatly along only one dimension and being exactly the same in all other dimensions are similar. This feels like an argument over definitions, but I disagree with the implication in this context that a single axis of differentiation is good enough for political parties.
You’re wrong when it comes to the mathematical definition (cosine similarity is looking for normalized dot product ≈ +1, not −1), and wrong in the important practical sense that “similar parties” should result in similar policy outcomes if elected, whereas strongly polarized parties result in quite different policy outcomes if elected. Stop doubling down.
I did not say cosine similar. I understand why you would take it as the default, but it is not the only measure of similarity, and there is no single mathematical definition of similarity. Don’t stoop to pedantry if you’re not going to be precisely correct yourself. (Normally I would not be rude like this, but you have exhausted my goodwill)
The policy outcomes of the two major US parties are similar. I think we have different perspectives on how varied outcomes should be between dissimilar parties. For the most part, both perpetuate the status quo.
One-dimensionality is similarity (lack of differentiation along other dimensions).
Strong correlation and strong anticorrelation are different things.
Non sequitor. In a high dimensional space, things varying greatly along only one dimension and being exactly the same in all other dimensions are similar. This feels like an argument over definitions, but I disagree with the implication in this context that a single axis of differentiation is good enough for political parties.
You’re wrong when it comes to the mathematical definition (cosine similarity is looking for normalized dot product ≈ +1, not −1), and wrong in the important practical sense that “similar parties” should result in similar policy outcomes if elected, whereas strongly polarized parties result in quite different policy outcomes if elected. Stop doubling down.
I did not say cosine similar. I understand why you would take it as the default, but it is not the only measure of similarity, and there is no single mathematical definition of similarity. Don’t stoop to pedantry if you’re not going to be precisely correct yourself. (Normally I would not be rude like this, but you have exhausted my goodwill)
The policy outcomes of the two major US parties are similar. I think we have different perspectives on how varied outcomes should be between dissimilar parties. For the most part, both perpetuate the status quo.