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

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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.
Funding Information
  • H2020 European Research Council (H2020-769142, H2020-825619)
  • H2020 European Research Council (H2020-872944)
  • Ministerio de Economía y Competitividad (PID2019-104156GB-I00)
  • Generalitat de Catalunya (2017 SGR 172)
  • Agence Nationale de la Recherche (ANR-20-CE23-0018)
  • Consejo Superior de Investigaciones Científicas

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