Inferring a hierarchical majority-rule sorting model

Real decision problems often involve a multitude of sub-problems that are intertwined and that need to be solved together in order to provide a global recommendation. A hierarchical structure may be used to represent such problems and we propose an indirect elicitation approach when each underlying problem can be modeled as a majority-rule sorting problem. We limit our study to a two level hierarchy structure, where the bounding profiles of the bottom layer are provided while those of the top layer need to be inferred. We propose a mathematical program to infer these profiles as well as the criteria weights and majority thresholds of all considered models. We test this program on generated benchmarks in order to evaluate its performance and find its limitations. The approach may furthermore be easily extended to more complex hierarchical structures.