More Complex Formulae of Generalized Exchange [and Comments and Replies]
John R. Atkins, Alan Barnard, Ira R. Buchler, Gisèle De Meur, David B. Eyde, Michael Fischer, Paul J. M. Jorion, Jordan Rustad · Current Anthropology · 1981
Levi-Strauss has argued that any further development of the principles of marriage-as-exchange upon which Les structures elementaires de la parente is premised towards a truly general theory of kinship and marriage must await a solution to the formal difficulties posed by the analysis of even the so-called Crow-Omaha systems. Hence the only viable option currently available would be to apply statistical methods to the study of the essentially probabilistic system of exchange events in such "more complex" structures. In this paper a different approach is adopted and a complete family of nonstatistical models of generalized exchange is developed to bridge the gap between Levi-Strauss's elementary structures and the Crow-Omaha systems. The set of models (wich includes structures with unilateral cross-cousin marriage as limiting cases) is generated by means of a recursive definition of exchange: marriages which occur in one generation are used to determine the sequence of exchanges in the following generation or exchange cycle. The exchange model is then related to existing mathematical models of kinship structures and all possible models with generalized exchange are derived for n (the number of descent lines) equal to or less than 9.