Robust Ordinal Regression for Subsets Comparisons with Interactions

In this preference elicitation setting, our focus is on determining the parameters of a decision model that accurately captures the pairwise preferences of a Decision Maker (DM) over subsets, by comparing subsets of elements. The preferences are depicted using a highly adaptable model whose versatility stems from its ability to incorporate positive or negative synergies between elements [24]. Moreover, we provide an ordinally robust approach, in the sense that the preferences we infer do not rely on arbitrarily specified parameter values, but on the set of all parameter values that are compatible with the observed preferences. Importantly, another distinctive feature of our approach is its ability to learn the parameter set itself (not only the values of parameters). The preference model we consider can be used in different contexts, depending on the nature of the subsets we are comparing. The subsets are represented by binary vectors, showing the presence or absence of an element in the subset. The elements of a subset can be for example: individuals (in the comparison of coalitions, teams, etc.), binary attributes (in the comparison of multiattribute alternatives), objects (in the comparison of subsets in a subset choice problem), etc. For illustration, a toy example of such an elicitation context could be a coffee shop trying to determine its customers' favorite frozen yogurt flavor combination by offering them to test a small number of flavor combinations rather than having them taste each combination.