Cox’s risk matrix theorem and its implications for project risk management

One of the standard ways of characterizing risk on projects is to use matrices which categorize risks by impact and probability of occurrence. These matrices provide a qualitative risk ranking in categories such as high, medium and low. Tony Cox shows that the qualitative risk ranking provided by a risk matrix will agree with the quantitative risk ranking only if the matrix is constructed according to certain general principles. This post is devoted to an exposition of these principles and their consequences.