  The article is devoted to the problem of inconsistency in the pairwise
comparisons based prioritization methodology. The issue of "inconsistency" in
this context has gained much attention in recent years. The literature provides
us with a number of different "inconsistency" indices suggested for measuring
the inconsistency of the pairwise comparison matrix (PCM). The latter is
understood as a deviation of the PCM from the "consistent case" - a notion that
is formally well-defined in this theory. However the usage of the indices is
justified only by some heuristics. It is still unclear what they really
"measure". What is even more important and still not known is the relationship
between their values and the "consistency" of the decision maker's judgments on
one hand, and the prioritization results upon the other. We provide examples
showing that it is necessary to distinguish between these three following
tasks: the "measuring" of the "PCM inconsistency" and the PCM-based "measuring"
of the consistency of decision maker's judgments and, finally, the "measuring"
of the usefulness of the PCM as a source of information for estimation of the
priority vector (PV). Next we focus on the third task, which seems to be the
most important one in Multi-Criteria Decision Making. With the help of Monte
Carlo experiments, we study the performance of various inconsistency indices as
indicators of the final PV estimation quality. The presented results allow a
deeper understanding of the information contained in these indices and help in
choosing a proper one in a given situation. They also enable us to develop a
new inconsistency characteristic and, based on it, to propose the PCM
acceptance approach that is supported by the classical statistical methodology.
