  In this paper we argue that conventional unitary-invariant measures of
recommender system (RS) performance based on measuring differences between
predicted ratings and actual user ratings fail to assess fundamental RS
properties. More specifically, posing the optimization problem as one of
predicting exact user ratings provides only an indirect suboptimal
approximation for what RS applications typically need, which is an ability to
accurately predict user preferences. We argue that scalar measures such as RMSE
and MAE with respect to differences between actual and predicted ratings are
only proxies for measuring RS ability to accurately estimate user preferences.
We propose what we consider to be a measure that is more fundamentally
appropriate for assessing RS performance, rank-preference consistency, which
simply counts the number of prediction pairs that are inconsistent with the
user's expressed product preferences. For example, if an RS predicts the user
will prefer product A over product B, but the user's withheld ratings indicate
s/he prefers product B over A, then rank-preference consistency has been
violated. Our test results conclusively demonstrate that methods tailored to
optimize arbitrary measures such as RMSE are not generally effective at
accurately predicting user preferences. Thus, we conclude that conventional
methods used for assessing RS performance are arbitrary and misleading.
