 Any dataset that satisfies  (RH)  will be called row-homogenous. By contrast, for any given set of proportions violating condition  (RH),  we can find datasets exhibiting these very same proportions such that AR indeed occurs (by fiddling with the size of the subpopulations; Lemma 3.1 in Mittal 1991). However, neither row homogeneity, nor the analogous condition of column homogeneity, nor their conjunction is sufficient for avoiding the amalgamation paradox AMP.