We introduce a fairness criterion that we call Spanning. Spanning i) is implied by Calibration, ii) retains interesting properties of Calibration that some other ways of relaxing that criterion do not, and iii) unlike Calibration and other prominent ways of weakening it, is consistent with Equalized Odds outside of trivial cases.

I discuss the epistemic status of algorithmic predictions in the legal realm. My main claim is that algorithmic predictions do not give us knowledge, not even probabilistic knowledge. The situation, however, is relevantly different from the one in which we find ourselves at the time of assessing statistical evidence in general, and it is rather related to the fact that algorithmic fairness in legal contexts is essentially undetermined. In the light of this, we have to settle for justified beliefs and (...) justified credences. I end by drawing some morals for the Knowledge Norm of action. (shrink)

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

This note contains a corrective and a generalization of results by Borsboom et al. (2008), based on Heesen and Romeijn (2019). It highlights the relevance of insights from psychometrics beyond the context of psychological testing.