Converting preferences to ratings

Question

Suppose I have a list of (e.g.) restaurants. A lot of users get a list of pairs of restaurants, and select the one of the two they prefer (a la hotornot).

I would like to convert these results into absolute ratings: For each restaurant, 1-5 stars (rating can be non-integer, if necessary).

What are the general ways to go with this problem?

Thanks

Answer 1

I would consider each pairwise decision as a vote in favor of one of the restaurants, and each non-preferred partner as a downvote. Count the votes across all users and restaurants, and then sort cluster them equally (so that that each star "weighs" for a number of votes).

Answer 2

Elo ratings come to mind. It's how the chess world computes a rating from your win/loss/draw record. Losing a matchup against an already-high-scoring restaurant gets penalized less than against a low-scoring one, a little like how PageRank cares more about a link from a website it also ranks highly. There's no upper bound to your possible score; you'd have to renormalize somehow for a 1-5 star system.