
Accession Number : AD0709874
Title : NOTES ON COMBINATORIAL MATHEMATICS: A DERIVATION OF A MEASURE OF RELATIVE BALANCE FOR SIGNED DIGRAPHS AND A CHARACTERIZATION OF EXTENSIVE RATIO SYSTEMS,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Norman,Robert Z. ; Roberts,Fred S.
Report Date : JUN 1970
Pagination or Media Count : 65
Abstract : In order to extend the Heider and CartwrightHarary theory of balance in social structures (signed digraphs), a measure of relative balance is needed which is derived from some plausible axioms and which reflects the balance ordering, i.e., the relation that one social structure is more balanced than another. This study approaches the problem indirectly by first axiomatizing a measure of distance and then relating balance to distance. It is shown that the axioms determine the balance ordering uniquely, subject to the specification of a certain parameter. This parameter is interpreted and some brief remarks are given on how it can be chosen. The measure of balance is then applied to a particular sociological situation. The problem of axiomatizing the balance ordering more directly is approached by formulating a second axiomatization that results in the same representation theorem and also solves the problem of axiomatizing extensive ratio systems. (Author)
Descriptors : (*SOCIAL SCIENCES, *COMBINATORIAL ANALYSIS), GRAPHICS, THEOREMS
Subject Categories : Sociology and Law
Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE