A ratio scale metric and the compatibility of ratio scales: The possibility of arrow's impossibility theorem

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Nov, 1994

Journal: Applied Mathematics Letters
Vol.: 7- Issue: 6- Pages: 51-57

Abstract: We develop a metric for ratio scales and explore the notion of compatibility of two sets of measurements of a set of objects or properties on a ratio scale. We briefly address Arrow's impossibility theorem. We maintain that it is not as impossible as claimed when, as in reality, a certain degree of inconsistency and incompatibility are allowed.

Keywords: Ratio scale, Metric, Compatibility, Impossibility, Group decision making, Diagnosis