Abstract

The previous chapters display a close similarity between probability and ranking theory. This calls for in-depth analysis of their relation. Various ways of formally integrating ranks and probabilities are discussed. It is argued that non-standard probabilities are disproportionate, that Popper measures are unsatisfactory (for the same reasons as AGM belief revision theory), and that the best unification is provided by so-called probabilified ranking functions. Still, the preferred attitude is so-called methodological separatism. The substantial convergences and divergences of ranks and probabilities are then discussed under the experiential, the inferential, the behavioral, the truth, the reality, and the objectivity aspect. Since the behavioral aspect is not further dealt with in the book, an appendix presents the so far best account of decision theory in ranking-theoretic terms.