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I don’t think this is it? Imagine a model where true scores (0-100) are X, and perceived scores are Y = X + 10 + random error, ie below avg people don’t think they are better than avg and don’t have more of a bias than above avg people. This will generate a DK-like chart.
The bias ensures that the intercept is greater than 0 and the random error ensures the slope is less than 1, and that’s all you need to reproduce the chart. You don’t need uniform belief in being better than average, you just need everyone to be the same amount of overconfident.
Notably you get a very similar chart if no one has any bias (everyone is correctly calibrated except for random error) or even if everyone has perfect belief about their own abilities but the test is noisy.
Yes, but relative to ability the same overconfidence bias in less knowledgeable people is a larger impact. Similar to how a flat welfare payment is progressive — it makes a bigger difference to people with less money.
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