Pairwise comparison tables within the deck of cards method in multiple criteria decision aiding

This paper deals with an improved version of the deck of cards method to render the construction of ratio and interval scales more “accurate” compared to the ones built in the original version. The improvement comes from the fact that we can account for a richer and finer preference information provided by the decision-maker, which permits a more accurate modeling of the strength of preference between different levels of a scale. Instead of considering only the number of blank cards between consecutive positions in the ranking of objects, such as criteria and scale levels, we consider also the number of blank cards between not consecutive positions in the ranking. This information is collected in a pairwise comparison table that is not necessarily built with precise values. We can consider imprecise information provided in the form of intervals and missing values. Since the provided information is not necessarily consistent, we propose also some procedures to help the decision-maker to make consistent her evaluations in a co-constructive way interacting with an analyst and reflecting and revising her judgments. A didactic example will illustrate the application of the method.