Ask HN: Help with algorithm for ranking content on interaction count and rating

TL;DR Content that has a low interaction count may have a 5 star rating because interaction is low. Content with higher interaction counts may have a 4.5 star rating and shows below content with 5 stars and lower interactions, even though it is probably the better choice. In our app we show a list of content (in our case Nightclubs) and allow users to sort based on 3 properties: Name, Rating, Favorite count. Name is self explanatory, it's just alphabetical ascending. Favorite count is also self explanatory, think of it as a like count and we sort descending. Rating is where it get's interesting... I'm looking for a fair "score" to rate venues on instead of simply rating. The problem with rating is venues that have more bookings are naturally going to have ratings below 5 stars. Our best venues with 100's of bookings have a rating around 4.6. This is a problem because most of our users are choosing to sort by rating, but those 4.6 rated venues with a ton of buyers are being shown below venues with minimal buyers that happen to have a 5 star rating. So my question, is there a fair algorithm that can take into account buy counts and rating to sort more naturally?