  Self-reinforcing feedback loops in personalization systems are typically
caused by users choosing from a limited set of alternatives presented
systematically based on previous choices. We propose a Bayesian choice model
built on Luce axioms that explicitly accounts for users' limited exposure to
alternatives. Our model is fair---it does not impose negative bias towards
unpresented alternatives, and practical---preference estimates are accurately
inferred upon observing a small number of interactions. It also allows
efficient sampling, leading to a straightforward online presentation mechanism
based on Thompson sampling. Our approach achieves low regret in learning to
present upon exploration of only a small fraction of possible presentations.
The proposed structure can be reused as a building block in interactive
systems, e.g., recommender systems, free of feedback loops.
