Can We Improve Without Worsening? Belief Change in Rational Rankings

Abstract

With the aim of providing a natural and expressive domain for defining change operators, we introduce the epistemic space of rational rankings. We show that this epistemic space is highly useful for understanding various aspects of belief dynamics, particularly those related to the improvement of new information. It enables us to define certain classes of improvement operators, a generalization of iterated revision operators, in a natural and intuitive way. A key feature of rational rankings is the possibility of defining improvement operators in such a way that the negation of the new information does not worsen. This is impossible within the frameworks of total preorders or ordinal conditional functions, two well-known epistemic spaces. Another notable aspect of this space is that the behavior of these operators can be characterized by a few simple equations and inequalities, whose meaning remains transparent. Additionally, there are no stationary states: The epistemic state resulting from applying an operator to a prior epistemic state and new information is always distinct from the prior state. Finally, we prove that this class of operators is indeed a subclass of improvement operators. Consequently, we show that these operators exhibit desirable behavior when iterated sufficiently, ultimately converging to Darwiche and Pearl revision operators.