  Pairwise comparison matrices are increasingly used in settings where some
pairs are missing. However, there exist few inconsistency indices to analyse
such incomplete data sets and even fewer measures have an associated threshold.
This paper generalises the inconsistency index proposed by Saaty to incomplete
pairwise comparison matrices. The extension is based on the approach of filling
the missing elements to minimise the eigenvalue of the incomplete matrix. It
means that the well-established values of the random index, a crucial component
of the consistency ratio for which the famous threshold of 0.1 provides the
condition for the acceptable level of inconsistency, cannot be directly
adopted. The inconsistency of random matrices turns out to be the function of
matrix size and the number of missing elements, with a nearly linear dependence
in the case of the latter variable. Our results can be directly used by
practitioners as a statistical criterion for accepting/rejecting an incomplete
pairwise comparison matrix.
