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An axiomatic approach to distance on partial orderings. (English) Zbl 0607.90003

We develop a set of axioms which uniquely determine a distance measure on the set of all partial orderings. The results presented generalize the previous work of K. P. Bogart [J. Math. Sociology 3, 49-67 (1973; Zbl 0303.92013); SIAM J. Appl. Math. 29, 254-262 (1975; Zbl 0326.92018)] and J. G. Kemeny and L. J. Snell [in: Math. Models in the Soc. Sciences, Ginn, New York, 9-23 (1962)]. While the matrix representation used herein differs from that of the above mentioned authors, our distance measure is shown to be equivalent to theirs when applied to the appropriate ranking subspaces.

MSC:

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