With a vast number of items, web-pages, and news to choose from, online
services and the customers both benefit tremendously from personalized
recommender systems. Such systems however provide great opportunities for
targeted advertisements, by displaying ads alongside genuine recommendations.
We consider a biased recommendation system where such ads are displayed without
any tags (disguised as genuine recommendations), rendering them
indistinguishable to a single user. We ask whether it is possible for a small
subset of collaborating users to detect such a bias. We propose an algorithm
that can detect such a bias through statistical analysis on the collaborating
users' feedback. The algorithm requires only binary information indicating
whether a user was satisfied with each of the recommended item or not. This
makes the algorithm widely appealing to real world issues such as
identification of search engine bias and pharmaceutical lobbying. We prove that
the proposed algorithm detects the bias with high probability for a broad class
of recommendation systems when sufficient number of users provide feedback on
sufficient number of recommendations. We provide extensive simulations with
real data sets and practical recommender systems, which confirm the trade offs
in the theoretical guarantees.Comment: Shorter version to appear in Sigmetrics, June 201