The actual DK result (which is much criticized, but that's a different issue) was actually a pretty much linear relationship between actual relative performance and self-estimated relative performance, crossing over at about the 70th percentile.
(Because there is more space below 70 than above, that also means that the very bottom performers overestimated their relative performance more than top performers underestimated, not because of any “double burden” (overstimation didn't rise faster as one moved below the crossover), but just because there was more space below the crossover point.
> Arguably the hypothesis that matches the data from the DK paper best is: "Everyone thinks they're average regardless of skill level"
If there was a perceptual nudge toward average relative performance, you'd expect a crossover at the median with a slope below 1, the nudge is toward a particular point above average.