Studying the dimensionality of political preferences

Keith Ellis writes:

I’ve been wondering about are the use of sophisticated mathematical techniques to discover what are the real-world political ideologies, starting without conventional preconceptions.

The core idea I had when this came to many years ago was by way of reading some technical articles about color vision. I was struck by one paper, which I could barely understand, which attempted to determine the “spatial” dimensionality of color vision…I recall vaguely that the conclusion was that it is best described in a 28 or so dimensional space. This connected up, conceptually in my imagination, with what was then the nascent specialty of the stuff involved in the Netflix prize—I can’t recall the technical term…preference modeling?

Anyway, it’s always bothered me that the libertarians’ two-dimensional planar political space was only slightly less simpleminded than the universal one-dimensional paradigm. Surely it’s the case that all political beliefs correlate in and cluster in interesting ways and, perhaps, might best be described in some, say, ten-dimensional space. Couldn’t we find these correlations and descriptive space and then look at those dimensions and ask: what are they?

I’m not a political scientist or a statistician. I hope you forgive my naivete and ignorance about all this. When imagining how one might go about this research, I thought perhaps one might first collect a very large sack of assertions/beliefs of political content. It’s hard to imagine how doing so could avoid all sorts of contaminating bias, but surely there’s “better” and “worse”. Given this large collection, then one would sample a large population on all these items. And then the mathematical work.

Surely something like this has been done many times. If so, then are the results just not very helpful or interesting, as I perhaps so naively assumed they must be? On the other hand, if they are helpful and interesting, why haven’t I heard of political analysis that utilizes something like this more empirical and much less preconceived and simpleminded conception of political ideologies?

My reply: There’s been a lot of work on this, more on the political ideologies of legislators than of voters. Data on legislative voting (“roll-call votes”) are easily available. The pioneers here are Howard Rosenthal, Keith Poole, and Nolan McCarty, and here’s their webpage. Back in the early 1990s, I think, there was a lot of discussion of the dimensionality of legislators’ ideology space, and a consensus that, most of the time, two dimensions captures most of it—with those two dimensions being different at different times. Really, though, there can’t be any “true” dimensionality here: the deeper you look, the more complexity you will find.

I’m pretty sure that similar work has been done on voters too, using various survey data. With 1500 people asked 100 questions each, you can apply standard multivariate statistical analyses or something more elaborate such as an ideal point model. What would be interesting is if you could do this over time and get some sense of how issues pop in and out of prominence. For example, in 2007, immigration was a huge issue, not so much since then.

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