IV - Emergence, Development, and Transformation of Kin-Based Exchange Systems

Summary

The chapters in this section trace the emergence of and changes in kin-based exchange systems by applying formal models and historical as well as ethnographic reconstruction. The first two chapters use combinatorial methods: Drawing on graph theory, Hage and Harary study the development of political systems in Oceania. Applying algebraic techniques to a problem of structuralist alliance theory, Tjon Sie Fat assesses the combinatorial possibilities of certain marital exchange rules in kinship systems. The last two chapters are also connected in regional focus: Wiessner and Tumu reconstruct from oral traditions the development of the Tee exchange system in the Highland of Papua New Guinea, drawing on their extensive collection of oral history sources. Görlich tackles social and economic structures and ensuing developments in the highlands and a fringe area of Papua New Guinea where he did field research. He draws on game theory to explain cooperation, bargaining, and coordination in societies without central authorities.

Hage and Harary study a combinatorial problem: detecting an optimal structure for describing the connectedness of networks. The graph-theoretic concept of a minimum spanning tree is such a device. This formal structure minimizes the total distance of nodes in a connected graph with no cycles. For detecting minimum spanning trees, the authors discuss three algorithms that are suitable for small networks (Kruskal's algorithm), large or dense networks (Prim's algorithm), and networks where each edge has a distinct value (Boruvka's algorithm being most efficient here).