- Abstract Research on preference elicitation and reasoning typically focuses on preferences over single objects of interest. However, in a number of applications the “outcomes” of interest are sets of such atomic objects. For instance, when creating the program for a film festival, editing a newspaper, or putting together a team, we need to select a set of films (resp. articles, members) that is optimal with respect to quality, diversity, cohesiveness, etc. This paper describes an intuitive approach for specifying preferences over sets of objects. An algorithm for computing an optimal subset, given a set of candidate objects and a preference specification, is developed and evaluated.