Abstract
It is often suggested that information retrieval systems should rank documents rather than simply retrieving a set. Two separate reasons are adduced for this: that relevance itself is a multi-valued or continuous variable; and that retrieval is an essentially approximate process. These two reasons lead to different ranking principles, one according to degree of relevance, the other according to probability of relevance. This paper explores the possibility of combining the two principles, but concludes that while neither is adequate alone, nor can any single all-embracing ranking principle be constructed to replace the two. The only general solution to the problem would be to find an optimal ranking by exploring the effect on the user of every possible ranking. However, some more practical approximate solutions appear possible.