I don't know how it works but if you have user buckets for basic political denominations

Users’ preferences are determined based on how they rate content, not on how they self-label.

In saying that a probability is used doesn't tell anythign on what the probability is based on. It just tells me that the result is a sliding scale between 0 and 1 but doesn't tell me whether it's a completely made up number.

I don’t think users need to know the actual equations (especially since the math is somewhat complicated). But they would easily find out if the numbers are made up (average probabilities for comments they like would be the same as for comments they don’t like).

Our recommendation system is based on principles of collaborative filtering. The average recommendation accuracy depends on the number of ratings in our database. With a relatively small number of users we can distinguish basic population clusters (e.g., left vs right or highbrow vs lowbrow). With a larger dataset we would be able to make more nuanced distinctions.