Prioritising Preference Relations

We describe some ideas and results about the following problem: Given a set, a family of "preference relations" on the set, and a "priority" among those preference relations, which elements of the set are best? That is, which elements are most preferred by a consensus of the preference relations which takes account of their relative priority? The problem is posed in a deliberately general way, to capture a wide variety of examples. Our main result gives sufficient conditions for the existence of `best' elements for an important instance of the problem: preference relations are pre-orders, the priority among them is a partial order, and the definition of best elements uses a generalisation of lexicographic ordering. 1 Introduction Often in computer science, we wish to pick from a set elements which satisfy certain properties. But often, the properties are conflicting, and we want to find elements which satisfy them as much as possible, or as many of them as possible. The situation may ..