A note on the AHP and expected value theory

It is shown here that one cannot simply take columns of numbers, normalize them and add to obtain results corresponding to operations in the AHP. This is what traditional expected value theory using a single scale would lead one to do. Care needs to be exercised. What one must do is to interpret the data represented by each column according to relative importance to a decision maker so that the alternatives under each criterion are pairwise compared according to the fundamental scale used to represent judgments. This procedure then leads to a set of vectors which belong to the same ratio scale and they can now be combined by using the weights of the criteria.