"Universal human nature" is a joke because humans aren't a single species. These are people whose ancestors didn't live in cities and don't have a conception of the basic logic of civilization - no ancestral history in civitas
Isn't it obvious by now that there is no Schelling point in "equality"? It's easily chipped away because it requires people to point out uncomfortable things about people who outnumber you and have votes and more importantly because it's not a well defined claim. 1/2
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Is there equality when people have different genetic endowments? When they have different backgrounds? "Well, this arbitrary amount of advantage from your family is ok, but this amount isn't" is the exact opposite of a Schelling point - no natural point to pick. 2/2
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"Equality under the Procedure" is? "Take noisy tests at face value; don't adjust for demographic regression to the mean" is Schelling if it's easier to agree on the Procedure than the regression coefficient. Maybe this is the part where you say "Manipulating procedural outcomes"?
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More generally (as a rationalist, I have NO interest in specific cases, and ESPECIALLY not politically-sensitive ones; I can ONLY articulate the GENERAL laws) populations are more predictable than individuals because of the law of large numbers. 1/2