An improved way to handle the strength of the discordance coalition in ELECTRE multiple criteria decision methods

This paper presents the results of two experiments involving real decision-makers. These experiments reveal a significant disparity between the credibility attributed by the ELECTRE III method to the outranking relation and that attributed by most surveyed decision-makers when the discordance coalition is stronger than the strict preference coalition. Such observed discrepancies challenge the conventional ELECTRE III outranking calculations. Based on this empirical evidence, we introduce a novel model for assessing the credibility index of the outranking approach. This model adjusts the original ELECTRE III formula to consider the relative importance of discordance coalition in comparison to the “weighted-size” of the strict preference coalition. This adjustment is operationalized through a simple piecewise increasing function, dependent on the “weighted-sizes” of both discordance and strict preference coalitions. Our proposed model not only upholds various consistency properties but also aligns with ELECTRE TRI methods and accommodates other adaptations of ELECTRE III designed for reinforced preferences and interactive criteria. Some simple examples illustrate the quality of the new model in the contexts of vote-based pair comparisons and multiple criteria ordinal classification.