On “Bostock vs Clayton County” and algorithmic discrimination.

https://www.theatlantic.com/ideas/archive/2020/06/what-because-of-sex-really-means/613099/

https://www.stanfordlawreview.org/online/the-many-meanings-of-because-of/

I’ve been reading a number of analyses of the landmark Gorsuch decision in the LGBTQ discrimination case. The articles linked above are very helpful in this regard, but I couldn’t help but also notice a very computational argument in Gorsuch’s reasoning that might be relevant for algorithmic discrimination.

The question at hand was whether firing someone because they were gay or trans could be viewed as being “because of sex” as per the Civil Rights Act. The opposing argument was that they weren’t fired because of their sex (or gender to be more precise) but because they were gay or trans, and since sexual orientation/gender identity was not protected in the Civl Rights Act explicitly, it’s not a violation.

The argument from the majority as I understand it can be translated mathematically as follows. Consider a function WTF (“whether to fire”) that seemingly takes two parameters (s, t): where s = X is “sex = X” and t = Y denotes either “attraction to people of gender Y” or “presents as gender Y”

(note that for the purpose of mathematical abstraction I’m violently conflating gender, sex and what it means to “present as gender Y”: these distinctions are very material but I can make the mathematical argument without needing to delve into the context).

The question is whether we can express WTF(s, t) = g(t) alone. As Gorsuch argues, this clearly cannot be the case else (in the case of Bostock), they’d have to also fire all women attracted to men, or (in the case of Stephens) all people presenting as women.

Clearly WTF(s, t) cannot also be written as h(s) (in fact if it were that would be blatant discrimination). In other words, the variable s contributes to the function outcome without being the sole determiner of it. ie in the parlance of explanations, the feature s has influence over WTFf(s, t).

And in the mind of the majority, this suffices to declare that this is invalid under Title VII.

It should be clear then what the implications for algorithmic discrimination are. On the positive side, it might be sufficient to show that a protected feature has some influence on the outcome (i.e a more disparate impact-like analysis). But before we get too excited about this, it’s unlikely that we’ll get the clear and stark difference between WTF(s, t) and g(t) that was present in this case, so it will remain to be seen what kind of ‘burden of scrutiny’ will come into play. Will it be as simple as a 4/5 rule?

Thoughts?

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