 With the possible exception of decision making (see however Giang and Shenoy, 2000 as well as Spohn 2017a, 2020), it seems that we can do everything with ranking functions that we can do with probability measures. Ranking theory also naturally gives rise to a notion of qualitative belief that incurs no Lottery-style paradoxes (see  Section 4.2.2).  This may be vital if we want to stay in tune with traditional epistemology. The treatment of ranking theory in this article has been, of necessity, rather compressed. For an excellent article-length introduction see Huber (2019). For an accessible book, see Huber (2020). For an extensive book-length treatment, with applications to many subjects in epistemology and philosophy of science, see Spohn (2012).