I think the motivation for the representability of some sets of conditional independences with a DAG is pretty clear, because people already use probability distributions all the time, they sometimes have conditional independences and visuals are nice.
On the other hand the fundamental theorem relates orthogonality to independences in a family of distributions generated in a particular way. Neither of these things are natural properties of probability distributions in the way that conditional independence is. If I am using probability distributions, it seems to me I’d rather avoid introducing them if I can. Even if the reasons are mysterious, it might be useful to work with models of this type—I was just wondering if there were reasons for doing that are apparent before you derive any useful results.
Alternatively, is it plausible that you could derive the same results just using probability + whatever else you need anyway? For example, you could perhaps define to be prior to if, relative to some ordering of functions by “naturalness”, there is a more natural such that and than any such that etc. I have no idea if that actually works!However, I’m pretty sure you’ll need something like a naturalness ordering in order to separate “true orthogonality” from “merely apparent orthogonality”, which is why I think it’s fair to posit it as an element of “whatever else you need anyway”. Maybe not.
Speaking personally, I think something like #1 is true on the grounds that I have seen many cases of white Australian people, often with considerable power, acting in excessively patronising and authoritarian ways towards Aboriginal people and I have no difficulty believing that similar things happen in the US.
However, I also do not think that racial disparities in outcomes are almost all caused by #1; in fact I think that probably less than 50% of almost any particular disparity is caused by #1. Thus, I think that outcome disparities are at best weak evidence for #1. Many people (notably Ibram X Kendi) say that in fact they are. I actually believe that the theory underlying this claim causes some of the authoritarian behaviour I observe. I think people reason something like this:
- We don’t want to be racist
—Differences in outcome indicate racism
—We must eliminate differences in outcome
—Eliminating differences in outcome requires substantial behavioural changes on the part of Aboriginal people
- Authoritarian strategies are the most reliable way we have to induce substantial behavioural changes
I think that overly authoritarian policy is often harmful.
I don’t know if DiAngelo endorses this claim—that outcome disparities are almost all caused by #1 - but claims like “being white is to know privilege” make me suspect that to some extent she is also reasoning backwards from outcome disparities to the existence of racismS. I think this is a big mistake!
I also think, with less confidence, that DiAngelo is not really popularising this theory but is rather explaining a theory that is already popular. Perhaps many people, like myself, think that this theory is flawed and that it is unfortunate that it is so popular. However, I suspect that they are making a mistake blaming DiAngelo for this. Criticism of her book could be a stand-in for criticism of this theory in general.
Maybe taking it further, I think that it’s possible that reasoning backwards from outcome disparities to racismS yields a flawed theory of what racismS is, because it’s a flawed inference to begin with. This might be why many people take issue with racismS rather than the premise (outcome disparities → racism), even though my best guess is that the premise comes first.