  A prevalent practice in recommender systems consists in averaging item
embeddings to represent users or higher-level concepts in the same embedding
space. This paper investigates the relevance of such a practice. For this
purpose, we propose an expected precision score, designed to measure the
consistency of an average embedding relative to the items used for its
construction. We subsequently analyze the mathematical expression of this score
in a theoretical setting with specific assumptions, as well as its empirical
behavior on real-world data from music streaming services. Our results
emphasize that real-world averages are less consistent for recommendation,
which paves the way for future research to better align real-world embeddings
with assumptions from our theoretical setting.
