Kinship: The Classificatory Kinship Page

Douglas R. White, University of California, Irvine
Polygyny (Standard_Cross-Cultural Sample)
Sexual Divsion of Labor

Abstract: A field experiment conducted in Central Australia in 1971-72 explored differences between what Aborigines actually did and what they said they did when anthropologists interviewed them. Fieldwork entailed observing behavior and recording it in numerically coded forms; analysis entails extracting patterns computationally that would not appear in traditional ethnographic data. This paper focuses on discrepancies between expected and observed with regard to descent, marriage and kinship. First it examines field methods and the resulting dataset, then it reviews a wide range of analytical methods that have been used to interpret the data. The alternative analytical methods reviewed here serve to test "competing hypotheses" about the nature and operation of Alyawarra descent, marriage and kinship. At the same time, however, the cumulative result of using these diverse methods has been increasingly complex and subtle understandings of previously unknown aspects of Central Australian social organization. The fact that the data continue to repay increasingly sophisticated analyses thirty years after they were recorded attests to the success of the field experiment.

Conclusions:

  • The Radcliffe-Brown normative model functions as a kind of "cognitive core" for the Alyawarra system of descent, marriage and kinship. It is not incorrect, but it is seriously incomplete and inadequate.
  • Examination of alternate models of Alyawarra social struWorkshop on Dynamics of groups and institutions: Their emergence, co-evolution and environment. Santa Fe Institute and the Research Centre of the Slovenian Academy of Sciences, from June 7 to June 11, 2004cture cannot be uniquely resolved into a single model but a nested model with a unique simplest structure embedded in models that are more complex. Each layer of models conforms to actual marriages that are in 98% agreement with the RB section memberships.
  • The elegance of the Atkins' double helix model is marred by the fact that patterns of marriage among the deceased are quickly forgotten and no longer cast their shadow as a constraint on future behaviors. Thus the "kinship system" can evolve dynamically across a class of network models influenced stochastically by age distributions at marriage in accordance with Tjon Sie Fat's algebraic model, and to incorporate non-Alyawarra lineages in ways that are incompatible with both the RB and the Atkins models, thereby violating the Axiom of Algebraic Closure. An open format model that does not require the assumption of Generational Closure is one of the nested models that provide a good fit to the ethnographic data.
  • The problem posed by the widespread extra-normative application of Omaha terms led us to discover recurring patterns in Alyawarra behavior that give the people a great deal of discretionary control over marriage by applying Omaha terms non-reciprocally in violation of the Axiom of Universal Reciprocity.
  • Not only was the field experiment successful, but our findings require some fundamental rethinking of models for Australian kinship. Abstract. A representational language for genealogical networks is developed that provides a better means of visualizing and analyzing some of the basic organizing principles of kinship. In contrast to the conventional genealogical diagram, with circles for females and triangles for males, a marriage link between pairs of opposite sex, and branches from that union to children, the p-graph uses a simpler graph-theoretic construction in which a node represents either a married couple or an unmarried individual, and arcs are directed from the parental couple to the nodes corresponding to their children. When a child is married, there will be two parental nodes, one for the wife's parents and one for the husband's. Thus the arcs (directed links from parents to children) in this graph need only be distinguished as to one of two types: those for parent(s) to sons and to daugthters, respectively. This representation makes for a compact graph in which different kinds of marriage (e.g., types of consanguineal marriages or relinkings to affines) will show up as cycles in the underlying undirected graph. Graph theoretical analysis of p-graphs can then easily order marriages through time and identify marriage patterns as changing configurations of marriage cycles through time, without distortion of the genealogical network itself.

    Abstract. Confusions between substantive and relational concepts of kinship as a social network have led to a number of problems that are clarified by a temporally ordered relational theory of network structure. The ordered-network approach gives rise to a novel means of graphing the social field of kinship relations, while allowing kinship to be locally defined in culturally relative terms. Its utility is exemplified in applications to kinships among US Presidents, Old Testament Canaanites, and native Australians of Groote Eylandt. The formal concepts treated in the mapping of kinship networks are: kinship axioms, parental graph structure, core, circuits of consanguineally and affinally linked kin, sides and divides, homeomorphic mappings, homomorphisms as potentially simplifying mappings of kinship, elementary structure, and order-structure. Representational theorems are proven about homeomorphisms, cores and circuits, and the ambiguity of elementary structures. The last set of theorems leads to clarifying and redefining some of the basic concepts of elementary, semi-complex and complex structures of kinship in terms of properties of generationally ordered networks. The conclusions of the formal argument are 'post-structural' in the narrow sense of demonstrating the need for specifying contingent historical processes in the structural analysis of kinship as a social field. The open-ended approach to change, one that is implied by the study of ordered structures that unfold in a temporal succession, connects to issues of population variability, selection, and evolutionary processes. The kinship structures that are mapped in this approach are not intended as any sort of complete representations of kinship 'systems', but merely as scaffoldings that help to bring into view kinship as a social field, providing a baseline for other mappings (which may be superimposed) of social processes such as communicative fields, exchange processes, transmission of learned behaviors, social rights and inheritance, political and religious succession, and the like.