Local Randomization
An alternative foundation for regression discontinuity: instead of continuity of conditional expectations (Continuity-at-Cutoff), assume there is a small window around the cutoff within which treatment assignment behaves as if randomly assigned — i.e. the running variable is unrelated to potential outcomes inside the window. This recasts the RD neighbourhood as a (local) randomized experiment, licensing finite-sample Fisherian randomization inference as well as large-sample methods. It is a stronger assumption than continuity and applies most naturally with discrete running variables or very narrow windows; the analyst must justify and select the window.
Relied on by
RDD (the local-randomization framework, as developed by Cattaneo, Frandsen, Titiunik and coauthors).