How many bits per rating?

Most recommender systems assume user ratings accurately represent user preferences. However, prior research shows that user ratings are imperfect and noisy. Moreover, this noise limits the measurable predictive power of any recommender system. We propose an information theoretic framework for quantifying the preference information contained in ratings and predictions. We computationally explore the properties of our model and apply our framework to estimate the efficiency of different rating scales for real world datasets. We then estimate how the amount of information predictions give to users is related to the scale ratings are collected on. Our findings suggest a tradeoff in rating scale granularity: while previous research indicates that coarse scales (such as thumbs up / thumbs down) take less time, we find that ratings with these scales provide less predictive value to users. We introduce a new measure, preference bits per second, to quantitatively reconcile this tradeoff.