Operators and Laws for Combining Preference Relations HAJNAL ANDR
Abstract:
The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain priority on the family of relations. We present four kinds of results. # We show that the lexicographic rule is the only way of combining preference relations which satisfies natural conditions (similar to those proposed by Arrow). # We show in what circumstances the lexicographic rule propagates various conditions on preference relations, thus extending Grosof's results. # We give necessary and sufficient conditions on the priority relation to determine various relationships between combinations of preferences. # We give an algebraic treatment of this form of generalized prioritization. Two operators, called but and on the other hand, are sufficient to express any prioritization. We present a complete equational axiomatization of these two operators. These results can be applied in the theory of social choice (a branch of economics), in non-monotonic reasoning (a branch of artificial intelligence), and more generally wherever relations have to be combined.
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