  Recommender systems often rely on models which are trained to maximize
accuracy in predicting user preferences. When the systems are deployed, these
models determine the availability of content and information to different
users. The gap between these objectives gives rise to a potential for
unintended consequences, contributing to phenomena such as filter bubbles and
polarization. In this work, we consider directly the information availability
problem through the lens of user recourse. Using ideas of reachability, we
propose a computationally efficient audit for top-$N$ linear recommender
models. Furthermore, we describe the relationship between model complexity and
the effort necessary for users to exert control over their recommendations. We
use this insight to provide a novel perspective on the user cold-start problem.
Finally, we demonstrate these concepts with an empirical investigation of a
state-of-the-art model trained on a widely used movie ratings dataset.
