If you wonder how we solved racism, we did it with simple and blunt rules everyone can follow such as "don¨t say the n-word" or "don't say that whites are better than blacks". People are still racist, but simple rules like that makes it harder to rile up a mob enough to burn down a black neighborhood (I know it happened in Tulsa, that is why I used it as an example since it probably wouldn't happen today).
Your theory explains why people misunderstand each other and are "doomed" to states of conflict due to how their minds work. It needs to go further to explain how good outcomes are produced despite conflict and misunderstanding.
Why do they accept "simple and blunt rules"? Where are these rules coming from? Why aren't the rules pushing people in the opposite direction? Are there other mechanisms beyond imposing simple and blunt rules on everyone? etc etc etc Don't be satisfied with your theory. It's a good start but keep digging.
Lets say you have an internal value function F which you use to judge peoples worth. If F is deterministic it means that for any observation X it produces a value F(X) = V, where V is some number.
With this function a rational person would be racist, as statistically whites are more educated than blacks, so maybe F(WHITE) = 0.7 and F(BLACK) = 0.4. People from this category say things like "Of course he failed the maths test, he is black!".
But lets say that your F output a probability distribution instead, then you'd recognize that the information is incomplete, so even though E(F(WHITE)) = 0.7 it could both be lower and higher. With this way to see the world the statement "Of course he failed the maths test, he is black!" doesn't make sense, as there are lots of black people who do very well in maths so your value function would include those possibilities as well.
Note that the talk about discrete categorization doesn't make sense, having real valued prejudice function based on loads of factors is still deterministic.
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In my experience most people go with the deterministic value function when not pressured. But when you say something like "Do you really mean that no black person could have done well on that test?" they typically acknowledge that there are some black people who would have done well, so they can still think probabilistic but it takes more effort. Maybe said effort is too much for the average person to apply it everyday so we are doomed to experience the current political strife forever.