Lévi-Strauss’s work on †cross-cousin marriage clearly owes a considerable debt to Radcliffe-Brown’s work on Australia. He both adopts Radcliffe-Brown’s three types of cross-cousin marriage as the three possible †elementary structures of kinship, and reanalyses Australian material in the first of the ethnographic sections of The Elementary Structures of Kinship. While Radcliffe-Brown regarded kinship as an extension of familial relationships to the tribal community in such a way as to achieve progressively higher levels of social integration, Lévi-Strauss regarded kinship as the product of a mode of thought which operated at a global (tribal) level, ordering people into opposed relationship categories such as ‘father’s father’ and ‘mother’s father’.
Lévi-Strauss followed Radcliffe-Brown in hypothesizing that the various types of Australian kinship system offered different scales of social integration, but considered the Murngin system provided the greatest potential for extensive social networks, because the chains of †matrilateral marriage alliance could be indefinitely extended, whereas the †bilateral Kariera and Aranda systems tend toward closure. Warner had shown that the Murngin had †patrilineal †moieties, but recognized seven patrilines in their kinship terminology. The two ‘outer’ lines, furthest from ego, both belonged to the opposite moiety to ego’s and therefore could not marry each other. This generated a notorious controversy, as to how many lines of descent actually existed in the Murngin kinship system. Although much of the Murngin debate was arcane, it did highlight an important ambiguity in Radcliffe-Brown’s model, where the line of descent in the kinship terminology, the land-owning group and the foraging band appear to be identically constituted. This ambiguity was resolved, at an academic level, in papers by Hiatt and †Stanner, but resurfaced in anthropological evidence presented on behalf of the first attempt by Aboriginal people to claim legal recognition of their title to land.