Closed-Loop View of the Regulation of AI: Equal Impact across Repeated Interactions

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, in particular, its unique stationary measure.