Abstract (EN)

While there are several languages for representingcombinatorial preferences over sets of alternatives,none of these are well-suited to the representationof ordinal preferences over sets of goods (which aretypically required to be monotonic). We proposesuch a language, taking inspiration from previouswork on graphical languages for preference representation, specifically CP-nets, and introduce conditional importance networks (CI-nets). A CI-netincludes statements of the form “if I have a set Aof goods, and I do not have any of the goods fromsome other set B, then I prefer the set of goods Cover the set of goods D.” We investigate expressivity and complexity issues for CI-nets. Then weshow that CI-nets are well-suited to the descriptionof fair division problems.