A solution to the Crow-Omaha problem and its implications for future research into social organization

Abstract

This thesis presents a solution to the Crow-Omaha problem as originally defined by Levi-Strauss (1966, 1969). By beginning with a fixed set of demographic conditions and a given form of Crow-Omaha marriage rules, and viewing the clan structure as being in a non-equilibrium state, it is possible to overcome the demographic problems which hampered Levi-Strauss' analysis of the Crow-Omaha systems. In particular, it is shown that in a finite and endogamous population demographic variation under Crow-Omaha exchange causes an imbalance in the size of clans and an actual reduction in clan numbers culminating in the convergence of the exchange system to a minimal structure with mechanical properties determined solely by the marriage rules. This result is independent of the initial pattern of exchange assumed in the analysis, or the particular demographic history of the population, the problems which originally impeded Levi-Strauss. The properties of the minimal structure can be used to explain several other features of Crow-Omaha societies, most importantly patterns of migration and clan fissioning. The results obtained here bear on the general theoretical question of the relationship between demographic and social variables, and suggest a direction for future research into problems of social organization. The analysis presented in this thesis is framed within the context of Navajo ethnography. Navajo social organization is not usually classified as Crow-Omaha because the kinship system is Iroquoian and clans are not corporate units. From the viewpoint of exchange, however, the Navajo system may actually be thought of as an ideal Crow-Omaha type, since the clans function almost exclusively in the regulation of marriage. By using the Navajo example in an initial analysis, any possible deviations from Levi-Strauss' model caused by clan hierarchization can be avoided. The effects of the convergence of the exchange structure within Navajo communities is examined by a comparison between ethnographic data and the results of computer simulations. A statistical tendency for marriage into one of the grandfathers' clans and the pattern of migration into Navajo communities are explained on the basis of the properties of the minimal exchange structure.