  In this paper, we discuss various problems in the usage and definition of
risk matrices. We give an overview of the general process of risk assessment
with risk matrices and ordinal scales. Furthermore, we explain the fallacies in
each phase of this process and give hints on which decisions may lead to more
problems than others and how to avoid them. Among those 24 discussed problems
are ordinal scales, semi-quantitative arithmetics, range compression, risk
inversion, ambiguity, and neglection of uncertainty. Finally, we make a case
for avoiding risk matrices altogether and instead propose using fully
quantitative risk assessment methods.
