I am trying to analyse the ratings for restaurants from a website. The rating system on the website is pretty simple: people can up-vote or down-vote.
The restaurant is then presented to website users with the number of votes it received and a percentage score (I am assuming this is simply an average of the votes: e.g. 2 up-votes and 1 down-vote will give a score of 66.7%).
Intuitively if I were to pick a restaurant to visit: I would rather pick one with a score of 90% and 100 votes than pick one with a score of 100% and 1 vote. Even though the former score is lower, I also know that the score won't be drastically affected by the next vote so I trust the score more. (Something Bayesian about this?)
How can a third metric (rating) be derived that combines score and number of votes to order restaurants not only by score but also by how trustworthy that score is?
I can think of a few empirical ways of doing this but they often result in me asking myself: What's better between (75%, 10 votes) and (80%, 8 votes)? Which isn't as obvious as the example above. Is there a more formal way to answer this question?