It is well known, and without controversy, that in experiments with randomization at the individual or unit level, stratiﬁcation on covariates is beneﬁcial if these covariates are substantially correlated with the outcome. However, there is less agreement in the literature concerning the beneﬁts of stratiﬁcation in small samples if this correlation is potentially weak.
The comments regarding the relative merits of complete randomization, stratiﬁcation, and pairwise randomization can be divided into three strands. The ﬁrst concerns precision of point estimates. The second argument focuses on statistical power of tests of the null hypothesis of no eﬀects. The third refers to the statistical limitations regarding the analysis of pairwise randomized experiments.
The argument that pairing leads to a reduction in accuracy is somewhat counterintuitive: if one constructs pairs based on a covariate that is completely independent of the potential outcomes, then pairing is for all intents and purposes equivalent to complete randomization.