How to find the best rated items on a likert scale and how many ratings are enough

The collection and exploitation of ratings from users are modern pillars of collaborative filtering. Likert scale is a psychometric quantifier of ratings popular among the electronic commerce sites. In this paper, we consider the tasks of collecting Likert scale ratings of items and of finding the n-k best-rated items, i.e., the n items that are most likely to be the top-k in a ranking constructed from these ratings. We devise an algorithm, Pundit, that computes the n-k best-rated items. Pundit uses the probability-generating function constructed from the Likert scale responses to avoid the combinatorial exploration of the possible outcomes and to compute the result efficiently. Selection of the best-rated items meets, in practice, the major obstacle of the scarcity of ratings. We propose an approach that learns from the available data how many ratings are enough to meet a prescribed error. We empirically validate with real datasets the effectiveness of our method to recommend the collection of additional ratings.