AI RESEARCH
The Pok\'emon Theorem and other Fairness Impossibility Results
arXiv CS.AI
•
ArXi:2605.09221v1 Announce Type: cross Fairness impossibility results often look like distinct scalar incompatibility statements. We show that several share one RKHS geometry: fairness criteria are linear constraints on conditional mean embeddings, and unequal base rates make the law of total expectation overdetermine those constraints. This view yields four results. The Kleinberg--Mullainathan--Raghavan dichotomy needs only group-conditional unbiasedness, not full calibration.