Before revision:  While the resulting sampling design is sometimes described as akin to  locally randomized experiment in a neighborhood of the threshold, standard formal analyses do not make reference to probabilistic treatment assignment and instead identify treatment effects via continuity arguments.
After revision:  While the resulting sampling design is sometimes described as akin to a locally randomized experiment in a neighborhood of the threshold, standard formal analyses do not make reference to probabilistic treatment assignment and instead identify treatment effects via continuity arguments.