Efficient minimal preference change

In this article, we study a minimal change approach to preference dynamics. We treat a set of preferences as a special kind of theory, and define minimal change preference contraction and revision operations in the spirit of the Alchourrón, Gärdenfors, and Makinson theory of belief revision. We characterise minimal contraction of preference sets by a set of postulates and prove a representation theorem. We also give a linear time algorithm which implements minimal contraction by a single preference. We then define minimal contraction by a set of preferences, and show that the problem of a minimal contraction by a set of preferences is NP-hard.