[p0pcult]

we can say, ceteris paribus, p(successful outcome|white) > p(successful outcome|nonwhite). That's what I am claiming. It also is possible to say that p(successful outcome|nonwhite) > 0. In fact, both of these things can be true simultaneously.

[bumby]

Right, but aren't we after the joint probability if we're really talking about equity? I.e., we can't make strong claims about an outcome unless we factor in the joint probability across all dimensions.

So, to extend your example, we can't necessarily say p(successful outcome|white)*p(successful outcome|poor) > p(successful outcome|nonwhite)*p(successful outcome|wealthy) until we measure those other socioeconomic conditions. It gets more complicated when we consider they may not all be independent of one another.

And that's just one extra variable. As you say, most agree we are multifaceted individuals. Adding dimensions like p(successful outcome|disability) or p(successful outcome|female) further complicates this as do all the other variables of a social species. So we can't really make strong statements about outcomes of a system very well unless we measure across the entire system of variables. I think that's what people are poking at. We may be able to make conclusions about individual variables but that doesn't always translate to an accurate model of the system at large. It's interesting and perhaps useful, but certainly incomplete. It only works under a "ceteris paribus" assumption, which is to say: "it only works in contrived circumstances that don't reflect reality."