Very interesting article and statistical analysis, but I really don't see how it concludes that the DK effect is wrong based on the analysis. The fact that the DK effect emerges with _completely random data_ is not surprising at all - in this case the intuitive null hypothesis would be that people are good at estimating their skill, therefore there would be strong a correlation between their performance and self-evaluation of said performance. If the data weren't related, then this hypothesis isn't likely, which is exactly what DK means. And indeed if you look at the plots in the article (of the completely random data), they depict a world in which people are very bad at estimating their own skill, therefore, statistically, people with lower skills tend to overestimate their skills, and experts tend to underestimate it.
Also wanted to point out that in general there is no issue with looking at y - x ~ x, this is called the residual plot, and is specifically used to compare an estimate of some value vs. the value itself.
That being said, the author seems very confident in their conclusion, and from the comments seems to have read a lot of related analyses, so I might be missing something. ¯\_(ツ)_/¯
Also wanted to point out that in general there is no issue with looking at y - x ~ x, this is called the residual plot, and is specifically used to compare an estimate of some value vs. the value itself.
That being said, the author seems very confident in their conclusion, and from the comments seems to have read a lot of related analyses, so I might be missing something. ¯\_(ツ)_/¯