Abstract
A formal framework for ranking procedures is proposed. The case of interest is where relatively few items are to be ranked with a complex procedure and according to a large number of criteria. A typical example of this scenario is a competition where several companies bid for a contract, and where the selection of the winner is done with multiple criteria according to an intricate selection procedure. A case study of a bidding procedure is presented, and a logical theory for matrix algebra is proposed as the formal framework for working with Pairwise Comparisons.