Preference relations, transitivity and the reciprocal property

AbstractTheories that attempt to represent decision makers' preferences are usually based on the axiom of transitivity. On the other hand, Saaty's Eigenvalue Method of deriving ratio scales from pairwise comparisons is based on the assumption that the numerical preferences satisfy the reciprocal property. We show that this property cannot be derived from the usual set of axioms used to obtain order preserving value functions, but that they in turn are consequences of the reciprocal property