Categorical, Ratio, and Professorial Data: The Case for Reciprocal Rank (2312.12672v1)

Abstract: Search engine results pages are usually abstracted as binary relevance vectors and hence are categorical data, meaning that only a limited set of operations is permitted, most notably tabulation of occurrence frequencies, with determination of medians and averages not possible. To compare retrieval systems it is thus usual to make use of a categorical-to-numeric effectiveness mapping. A previous paper has argued that any desired categorical-to-numeric mapping may be used, provided only that there is an argued connection between each category of SERP and the score that is assigned to that category by the mapping. Further, once that plausible connection has been established, then the mapped values can be treated as real-valued observations on a ratio scale, allowing the computation of averages. This article is written in support of that point of view, and to respond to ongoing claims that SERP scores may only be averaged if very restrictive conditions are imposed on the effectiveness mapping.