  There has been much recent interest in the regulation of AI. We argue for a
view based on civil-rights legislation, built on the notions of equal treatment
and equal impact. In a closed-loop view of the AI system and its users, the
equal treatment concerns one pass through the loop. Equal impact, in our view,
concerns the long-run average behaviour across repeated interactions. In order
to establish the existence of the average and its properties, one needs to
study the ergodic properties of the closed-loop and its unique stationary
measure.
