On the dominant set selection problem and its application to value alignment

Decision makers can often be confronted with the need to select a subset of objects from a set of candidate objects by just counting on preferences regarding the objects’ features. Here we formalise this problem as the dominant set selection problem . Solving this problem amounts to finding the preferences over all possible sets of objects. We accomplish so by: (i) grounding the preferences over features to preferences over the objects themselves; and (ii) lifting these preferences to preferences over all possible sets of objects. This is achieved by combining lex-cel –a method from the literature—with our novel anti-lex-cel method, which we formally (and thoroughly) study. Furthermore, we provide a binary integer program encoding to solve the problem. Finally, we illustrate our overall approach by applying it to the selection of value-aligned norm systems.