We show that, when the three-way association level among the three binary variables, X, U-1 and U-2 is fixed, D-P = pr( X = 1 | U-1 = 1) - pr( X = 1 | U-1 = 0) increases as the cross-product ratio of U-1 and U-2 increases under the assumption that X is positively associated with U-1 and U-2. We then discuss some implications of this property.