There appears to be an amount of confusion relating to the difference between Roissy's binary hierarchy and my more graduated hierarchy. However, it's not difficult to distinguish between the two hierarchies, nor is there any contradiction between them. Roissy's hierarchy is solely sexual in nature, whereas mine is socio-sexual. Therefore, his two categories are supersets of my seven categories.
ALPHA: natural alpha, synthetic alpha, sigma, high beta, high lambda
BETA: low beta, delta, gamma, omega, low lambda
In order to distinguish the sexual supersets from the socio-sexual sets, I suggest that when referring to a Roissyan superset, all caps should be used. When referring to a socio-sexual set, use lowercase letters. So, there should be no more trouble confusing an ALPHA with an alpha. Now, there is room to discuss whether low betas should be distinguished from deltas or not, (I tend to feel that delta is such a broad category that it merits the distinction), and if lambdas even belong in the supersets considering that the supersets are defined with regards to sexual success with women rather than sexual success per se.
Regardless, the point remains that there is no intrinsic contradiction between the sexual and socio-sexual hierarchies. Roissy's hierarchy remains perfectly valid and it is all that is necessary for PUA-centric discussions of Game. After all, scoring is inherently binary in nature, as one either scores or does not score. However, the logical, and I would argue, necessary, expansion of Game into areas beyond the crimson arts requires a more articulated hierarchy that is eminently justified by the observation of human social dynamics.