Per Hage & Frank Harary

The Logical Structure of Asymmetric Marriage Systems

Per Hage & Frank Harary, The Logical Structure of Asymmetric Marriage Systems. — The logical structure of asymmetric marriage systems is examined with respect to four questions. (1) To what extent can transitivity (hierarchy) be neutralized through the formation of cycles? (2) How are transitive structures generated in cyclical systems? (3) How can systems be compared with respect to their degree of transitivity? (4) Are hypergamous systems necessarily nonprescriptive?

Parkin (1990) has proposed that the forms of hierarchy associated with prescriptive and non-prescriptive asymmetric marriage systems can be distinguished on the basis of their logical structure. In non-prescriptive systems, which by definition do not specify or institutionalize the choice of spouse, hierarchy has the form of a "ladder" and is transitive. In prescriptive systems — in Lévi-Strauss' s (1969) terminology "generalized exchange" or in Needham's (1987: 134) characterization, systems "constructed on the module of marriage with the mother's brother's daughter" — hierarchy has the form of a "circle" and is said to be intransitive. The implication is that generalized exchange is not inherently unstable as Lévi-Strauss maintains. Although few if any asymmetric prescriptive systems or systems of generalized exchange are actually intransitive, Parkin's analysis raises four important questions concerning their structure:

(1) To what extent can transitivity be neutralized through the formation of cycles?

(2) How are transitive structures generated in cyclic systems?

(3) How can different systems be compared with respect to their "degree of transitivity"?

(4) Are hypergamous systems necessarily non-prescriptive?

L'Homme 139, juil.-sept. 1996, pp. 109-124.