How to compare "grid/group model" and "geo-anthropological" model ?

In Cultural theory, considering only "four" positions means that there are, like in a logical square, two main opposed principles and two mediations. The two main principles are "individualism" and "hierarchism", because the first one is "empty" and the second one "full". The two other positions are mediations, because they are "half-full/half-empty".
Why has this difference between principles and mediations a strong anthropological meaning ? Because it reflects a cultural universal constant : Human beings constantly think and act through categories implied by langage. "Categories" just mean (as the greek etymology points it) making reality "falling" into closed entities, which existence is only guaranteed by contradiction, or systems of contradictions. For example, there is no "Rich" if there is no "Poor", and reversedly.
We can assume that, in the human historical destiny, very strong, pragmatical oppositions have passed through various contexts. According to me, it is the case of close and friendly relationships in the very small group (not to be confused with a sect) as opposed to societal necessities (alliances between groups, for instance). In our immense societies, this opposition is dramatic, and even tragical.
I am quite aware this opposition does not not strictly reflect the douglasian "Individualist/Hierarchist" line, but it helps to understand that a small number of very strong contradictions can last over eons. But, they could not last so long if they were not "mediated", and somehow relaxed by different styles of action between them. Two important styles appear immediatly and constantly in order to "moderate" the first "clash" : the first mediation is more "metaphorical", (artistic or religious), the second is based on authority of pure regulation. Again, these mediations do not exactly fit the sectarian/enclavist diagonal in the douglasian model. But they allow everybody to understand that, in every society, believing in a communautarian ideal is not exactly the way of reconciling individuals and groups that is choosen by a pure legal or organizational constraint. So, mediations are at the same time immediatly and constantly necessary, and very different in style.
That is my way of understanding and interpreting a cultural theory, and maintaining it in front of objections pointing at the small number it is using. "Two" is the destiny of the speaking primate, because speaking always means breaking reality in opposite directions, and '"four" is only the beginning of plurality, using mediations to make the human world tolerable. Indeed,"four" is not a limitation : it is the principle representing the fact that human positions must be symmetrical as far as they want to be respected. Equality, here, means "equity". For instance, a "well ordered society" (to quote Rawls) should be, in a cultural theory perspective, a social conversational field where there would be a balance between communautarian, societal, litigant and friendly/homely ways of building up social links. Please, think about this extension of douglasian concepts as an opportunity... to keep them alive and more recognized; it could also be useful to call for a pluralistic global society, as opposed to.. a world super-state .