Axiomatizations of inconsistency indices for triads
  Pairwise comparison matrices often exhibit inconsistency, therefore many
indices have been suggested to measure their deviation from a consistent
matrix. A set of axioms has been proposed recently that is required to be
satisfied by any reasonable inconsistency index. This set seems to be not
exhaustive as illustrated by an example, hence it is expanded by adding two new
properties. All axioms are considered on the set of triads, pairwise comparison
matrices with three alternatives, which is the simplest case of inconsistency.
We choose the logically independent properties and prove that they
characterize, that is, uniquely determine the inconsistency ranking induced by
most inconsistency indices that coincide on this restricted domain. Since
triads play a prominent role in a number of inconsistency indices, our results
can also contribute to the measurement of inconsistency for pairwise comparison
matrices with more than three alternatives.
