While there are several languages for representing combinatorial preferences over sets of alternatives, none of these are well-suited to the representation of ordinal preferences over sets of goods (which are typically required to be monotonic). We propose such a language, taking inspiration from previous work on graphical languages for preference representation, specifically CP-nets, and introduce conditional importance networks (CI-nets). A CI-net includes statements of the form “if I have a set A of goods, and I do not have any of the goods from some other set B, then I prefer the set of goods C over the set of goods D. ” We investigate expressivity and complexity issues for CI-nets. Then we show that CI-nets are well-suited to the description of fair division problems.

Authors

• Sylvain Bouveret
• Ulle Endriss
• Jérôme Lang CNRS, Université Paris Dauphine, PSL

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