Belief Change on Rational Rankings

We introduce a new epistemic space: the space of rational rankings. This space is very useful for understanding some aspects of belief dynamics. In particular, the issues which concern improving the new information. Thus, we define in a very clear and succinct way a class of operators capturing the fact that the new information is improved. An interesting feature of this space is that the behavior of these operators can be characterized through a few equations and inequalities which are very simple and whose meaning is transparent. We prove that these operators are indeed improvement operators. Moreover, we show that these operators have good behavior when they undergo a sufficient number of iterations. In such a case, they become Darwiche and Pearl revision operators.