  Recommender systems are present in many web applications to guide our
choices. They increase sales and benefit sellers, but whether they benefit
customers by providing relevant products is questionable. Here we introduce a
model to examine the benefit of recommender systems for users, and found that
recommendations from the system can be equivalent to random draws if one relies
too strongly on the system. Nevertheless, with sufficient information about
user preferences, recommendations become accurate and an abrupt transition to
this accurate regime is observed for some algorithms. On the other hand, we
found that a high accuracy evaluated by common accuracy metrics does not
necessarily correspond to a high real accuracy nor a benefit for users, which
serves as an alarm for operators and researchers of recommender systems. We
tested our model with a real dataset and observed similar behaviors. Finally, a
recommendation approach with improved accuracy is suggested. These results
imply that recommender systems can benefit users, but relying too strongly on
the system may render the system ineffective.
