  Recommender systems play a crucial role in mediating our access to online
information. We show that such algorithms induce a particular kind of
stereotyping: if preferences for a set of items are anti-correlated in the
general user population, then those items may not be recommended together to a
user, regardless of that user's preferences and rating history. First, we
introduce a notion of joint accessibility, which measures the extent to which a
set of items can jointly be accessed by users. We then study joint
accessibility under the standard factorization-based collaborative filtering
framework, and provide theoretical necessary and sufficient conditions when
joint accessibility is violated. Moreover, we show that these conditions can
easily be violated when the users are represented by a single feature vector.
To improve joint accessibility, we further propose an alternative modelling
fix, which is designed to capture the diverse multiple interests of each user
using a multi-vector representation. We conduct extensive experiments on real
and simulated datasets, demonstrating the stereotyping problem with standard
single-vector matrix factorization models.
