Controversial - the place to discuss controversial topics

I think it’s useful to construct simplified models to show how changing just one thing works without getting lost in the mire of other effects, counter-effects, and opportunities to twist the answer. Even if it’s unrealistic until you add those effects back in.

Well, I wouldn't say something rude like "your post is useless" even if I believed it (which I don't) but at the same time I'm kind of struggling to see how to apply your point seeing as it was made in the ideal hypothetical scenario. After we do add those effects back in like:

1. There isn't actually a race that's just inherently X% dumber and everything else equal.
2. Intelligence is a multifaceted thing. You can measure and average those facets and come up with a single number, but it doesn't really tell you much about how a person can practically apply "intelligence" or what they can accomplish with their "intelligence".
3. Tests like the IQ test have significant flaws and culture/education level can have a non-trivial effect on the result. So someone that was deprived of access to education might score lower even though they have the exact same intrinsic potential for intelligence as someone else that scored higher.

How do we relate the real situation to what you said?

trying to find an answer to the runaway loop of rational prejudice.

That's kind of the problem: Prejudice can seem rational in the simplified example that doesn't have any nuance. In reality though, there are too many factors to account for, too much missing data. So when someone introduces "Greens have 10% lower IQ scores" to the conversation it's virtually never going to be constructive. That's the point I was making originally.

In a more complex example, I’d have to deal with green kids growing up in worse conditions and anti-green prejudice opening a bigger gap between collective green success and collective purple success.

Indeed. Even a small discrepancy that wouldn't really have much practical effect could absolutely be magnified by bigotry. Again, I feel like this is kind of reinforcing my original point.

My math went like so:

My statistics knowledge isn't good enough to call you out (or confirm that you're correct). The 60-65 number you came up with sounded reasonable to me, so I don't really have a reason to argue about that.

However, if there’s a combined IQ test in this world, the standard deviation is probably larger than the 15 that real IQ tests aim for and that would wreck my math.

You mean a test that includes both the greens and purples? I'm not sure how that would be relevant in this specific scenario since we're talking about comparing greens and purples.