Integrating confidence and preservation of information in the preference elicitation process: A lexicographic order approach for inconsistent judgments

The Pairwise Comparison Table for the Deck of Cards Method enables the elicitation of preference parameters through an interactive process between an analyst and a Decision-Maker (DM). As in other preferences elicitation processes in Multiple Criteria Decision Aiding (MCDA) problems, this methodology can result in several inconsistent judgments. One way to address this concern is to use Linear Programming (LP) techniques to find solutions that minimize the number of initial inconsistent judgments that must be modified to restore consistency. However, since this approach does not allow further differentiating solutions, it can be inefficient in decision problems with multiple inconsistent information and several distinct solutions to overcome such inconsistencies. To enhance the decision-making process and to suggest solutions based on enriched information, we propose a new procedure for addressing inconsistent judgments based on two additional criteria to complement the minimum cardinality criterion. While the first additional criterion concerns the confidence level of the DM in their initial judgments, the second seeks to minimize the modifications made to the initial judgments to distort them as little as possible. Solving the three criteria in a specific LP-based lexicographic order defined by the DM makes it possible to determine a comprehensive ranking of eligible solutions to restore consistency. Proposing these solutions to the DM according to their position in the ranking enables revising the initial inconsistent judgments more efficiently. The new methodology also considers the possibility of missing confidence information, which can decrease the cognitive effort of the DM in real-world decision problems when eliciting preferences.