I just ran across an interesting working paper by P.J. Healy and D.A. Moore, providing a potenial explanation for several forms of overconfidence.
We study three distinct measures of overconfidence: (1) overestimation of one’s performance, (2) overplacement of one’s performance relative to others, and (3) overprecision in one’s belief about private signals. A new set of exper- iments verifies a strong negative link between overestimation and overprecision that depends crucially on task difficulty (the ‘hard-easy’ effect). We present a simple Bayesian model in which agents are uncertain about the underlying task difficulty. This model correctly predicts the observed regularities. Thus, we capture several observed patterns of overconfidence without assuming any implicit behavioral biases.
Intuitively it still seems like a perfectly rational agent should be able to factor in the fact the given method will make them overconfident. That said I didn't work through all the math so it's possible I'm missing something, probably something related to bias-varaince trade offs.