While I agree that `P(loan | race=1, black_zip) = P(loan | race=2, black_zip) = 0` does indeed satisfy the condition, I think the kind of discrimination it crea

While I agree that `P(loan | race=1, black_zip) = P(loan | race=2, black_zip) = 0` does indeed satisfy the condition, I think the kind of discrimination it creates is in some sense out of scope. This is because if P(loan | black_zip) is profitable > 0, any bank primarily motivated by profit will approve such loans. [this is the statement I believe you meant] If P(loan | black_zip) isn't profitable > 0 after correcting for race, this would mean is that the neighborhood itself signaled something about the person's likelihood of paying back the loan. Perhaps theft is very common, employment is very sparse or seasonal, vandalism/arson of property is common, etc... because we already corrected for race it amounts to saying "don't approve housing loans for neighborhoods where people regularly burn down houses" or similar. This doesn't seem discriminatory to me. So while I do agree there are discriminatory issues not addressed by the formalism, your example seems to be handled by using the normal economic models for what decisions a bank should make given a model P(loan).