Stability, Fairness and the Pursuit of Happiness in Recommender Systems

Abstract

Top-k personalized recommendations are ubiquitous, but are they stable? We study whether, given complete information, buyers and sellers prefer to participate in matches formed by top-k recommendations rather than pursuing offline matches among themselves. When there are no constraints on the number of times an item is recommended, we observe that top-k recommendations are stable. When exposures are constrained, e.g., due to limited inventory or exposure opportunities, stable recommendations need not exist. We show that maximizing total buyer welfare under unit exposure constraints is stable, Pareto optimal and swap-envy free for orthogonal buyers, identical buyers, and buyers with dichotomous valuations. Most of these properties are retained under arbitrary exposure constraints. Finally, we consider variants of common recommendation strategies and find that they lead to substantial instability and envy in three real-world datasets. Among them, maximizing buyer welfare leads to the most stable outcomes and near-zero swap-envy.

Keywords: Recommender systems, Stable matching, Fairness, Envy free, Choice models

JEL Classification: C78