The Analytic Hierarchy Process: wash criteria should not be ignored

In this short paper it is shown that care is required to perform the appropriate normalisation needed to derive the right set of priorities from paired comparisons when criteria are added or deleted in a decision problem. This is particularly true for criteria with respect to which the alternatives have equal priorities and may be thought by someone to be of no consequence in ranking the alternatives. It is easy to see that small perturbation of the equal values of the alternatives with respect to an overwhelmingly important criterion can make a substantial difference to the final priorities of the alternatives if that criterion, called a wash criterion, is blindly deleted from the set of criteria. Background discussion and examples by some authors who did not examine it in the depth needed to understand its consequences are given to demonstrate how to deal with this artificially concocted idea.