Studying a set of properties of inconsistency indices for pairwise
  comparisons
  Pairwise comparisons between alternatives are a well-established tool to
decompose decision problems into smaller and more easily tractable
sub-problems. However, due to our limited rationality, the subjective
preferences expressed by decision makers over pairs of alternatives can hardly
ever be consistent. Therefore, several inconsistency indices have been proposed
in the literature to quantify the extent of the deviation from complete
consistency. Only recently, a set of properties has been proposed to define a
family of functions representing inconsistency indices. The scope of this paper
is twofold. Firstly, it expands the set of properties by adding and justifying
a new one. Secondly, it continues the study of inconsistency indices to check
whether or not they satisfy the above mentioned properties. Out of the four
indices considered in this paper, in its present form, two fail to satisfy some
properties. An adjusted version of one index is proposed so that it fulfills
them.
