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Dimensionality of Politics

Posted 4 months ago
4 Replies

Why not mention "polarization"? If you have data for congress from 60's to now, you can take the max value from the scree plot as a function of time. Perhaps that's leading to a hypothesis: polarization of the voting spectrum drives loss of nuance in political opinion space. That seems straightforward to prove from a maths point of view, but is likely more difficult to even support at a sociological level.

It would also be interesting to see what else two-party-based political polarization could drive, or at least strongly correlate with. For example, here's another hypothesis: Once the spectrum of law-making is divided into mutual antagonism between left and right, the process of law-enforcement will follow suit by adapting jurisprudence to harsh persecution more often than to lenient forgiveness (never mind the now-forgotten maxims "innocent until proven guilty" and "cruel and unusual punishment", the cancel culture and the mob mentality have both done away with all of that "useless antiquarian thought"!).

There's probably not enough good data about politics and trials during the French revolution, but there are a few well known cautionary tales, the worst one I know is about Antoine Lavoisier who--in addition to being a humanitarian scientist--was guillotined one year and completely exonerated the next.

POSTED BY: Brad Klee
Posted 4 months ago

Thanks for the great analysis and information. The concept of dimensionality is really good to me.

I would like to see PCA/FA/SEM with various rotation options in Mathematica. In general, PCA is a first step to understand the latent structure and then we usually apply PCA/Factor analysis (FA) with various rotations (e.g., varimax rotation) to further simplify the latent structure. Then, SEM (structural equation modeling) is applied, which is a confirmatory analysis or a hypothesis testing analysis. PCA/FA starts with data to derive latent structure (exploratory analysis) while SEM starts with a hypothesis on latent structure and validate it with data (confirmatory analysis).

I found a paper on SEM written by Reinhard Oldenburg, using MMA.

PLS (partial least square) is a widely used method in chemometrics that is recently expanded to handle the SEM, called PLS-SEM. I use the PLS frequently in automotive and would like to see the PLS in MMA also.

Maybe Anton Antonov or Andrea Lausche could work on these (I watched their video/web pages often)?

Here is PLS written in MMA.

Here is Wikipedia sites:

  1. Wikipedia on PLS (
  2. Wikipedia on SEM (
  3. Wikipedia on FA (
  4. Wikipedia on PCA (
POSTED BY: Sangdon Lee

To the list of dimension reduction algorithms I would add Independent Component Analysis (ICA) and Non-Negative Matrix Factorization (NNMF). There are resource functions and a paclet that combines them:

So, presumably, I can add other dimension reduction algorithms to "DimensionReducers". I am generally interested in doing that, but that requires for each algorithm to adopt a special mindset for week or two, and, usually, have a special diet. (Well, for me, at least.)

Shangdon, thanks for mentioning my work!

POSTED BY: Anton Antonov

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