Deck of Cards method for Hierarchical, Robust and Stochastic Ordinal Regression

TL;DR

The paper extends the Deck of Cards Method (DCM) to hierarchical, robust, and stochastic ordinal regression by integrating scaling and ordinal-generalization capabilities. It leverages Robust Ordinal Regression (ROR) and Stochastic Multicriteria Acceptability Analysis (SMAA) to generate admissible evaluations across the full set of value functions compatible with the decision maker's preferences, including $w$-weighted sums, linear/monotone, and Choquet integral forms. It accommodates hierarchical criteria and allows the DM to provide precise or imprecise information at different levels, producing outputs such as Rank Acceptability Indices (RAIs), Pairwise Winning Indices (PWIs), and barycenter-based aggregations. The didactic Italian-regions example demonstrates applicability to Circular Economy, Innovation-Driven Development, and Smart Specialization, illustrating uncertainty-aware, DM-tailored support for regional policy evaluation.

Abstract

We consider the recently introduced application of the Deck of Cards Method (DCM) to ordinal regression proposing two extensions related to two main research trends in Multiple Criteria Decision Aiding, namely scaling and ordinal regression generalizations. On the one hand, procedures, different from DCM (e.g. AHP, BWM, MACBETH) to collect and elaborate Decision Maker's (DM's) preference information are considered to define an overall evaluation of reference alternatives. On the other hand, Robust Ordinal Regression and Stochastic Multicriteria Acceptability Analysis are used to offer the DM more detailed and realistic decision-support outcomes. More precisely, we take into account preference imprecision and indetermination through a set of admissible comprehensive evaluations of alternatives provided by the whole set of value functions compatible with DM's preference information rather than the univocal assessment obtained from a single value function. In addition, we also consider alternatives evaluated on a set of criteria hierarchically structured. The methodology we propose allows the DM to provide precise or imprecise information at different levels of the hierarchy of criteria. Like scaling procedures, the compatible value function we consider can be of a different nature, such as weighted sum, linear or general monotone value function, or Choquet integral. Consequently, the approach we propose is versatile and well-equipped to be adapted to DM's characteristics and requirements. The applicability of the proposed methodology is shown by a didactic example based on a large ongoing research project in which Italian regions are evaluated on criteria representing Circular Economy, Innovation-Driven Development and Smart Specialization Strategies.