Abstract
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.
Highlights
Some actual-world decision making problems require to select an array of elements despite decision makers only counting on preferences over the elements’ features
We assume that there is a set of candidate norms N and we aim to find the set of norms that better aligns with the moral values of the society
Several social ranking solutions have been proposed, such as: a grounding function based on the ceteris paribus majority principle [11]; a grounding function based on the notion of marginal contribution [12]; two rankings based on the analysis of majority graphs and minmax score [1]; or the lex-cel ranking function [6], which is based on lexicographical preferences
Summary
Some actual-world decision making problems require to select an array of elements despite decision makers only counting on preferences over the elements’ features. Some examples are committee selection [13], or college admissions [9, 17]. Considering this last example, picture the following situation. The head master leverages on the admission policy of the school, which, for instance, prioritises some minorities, or fosters impoverished neighbourhoods. Such policies can be cast as preferences over the students’ features. The head master lacks of a straightforward manner to rank all possible sets of students, since these features somehow pose a multi-criteria problem. There is a further dimension of complexity: some sets may not be eligible
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