RDD is a technique that originated in the 1960s by Thistlewaite & Campbell and re-invented by Goldberger (1972) and Tallmadge & Horst (1976). There are 2 types of RDD - Sharp RD vs. Fuzzy RDD; similar underlining concepts but here I will focus on Sharp RDD.
In Sharp RDD, randomization is generated by a selection variable (running variable) the caused a discontinuity based a pre-determined cut-off score and consequently estimate a causal treatment effect.
My discussion/question is: Is this "discontinuity" enough to strongly assume randomization and estimation of causal treatment effect without any bias (selection bias, measurement error, simultaneity, or any endogeneity)?