The paper compares a variety of well known set theoretic consistency conditions on choice functions with the two that have been introduced by the author in an earlier paper [J. Quant. Econ. 1, 265-272 (1985)]. The two conditions are non-trivial generalizations of choice functional transitivity and quasi-transitivity respectively. The paper shows if the two conditions are individually stronger than or weaker than or logically independent of 14 other conditions including the rationalisability by an ordering, path independence, the conditions \(\alpha\) and \(\beta\), idemmorphism, absorbance and superset. The relative strengths of all the 16 conditions have been summed up at the end by an implication diagram.