We study the problem of designing a mechanism to rank items in forums by making use of the user reviews such as thumb and star ratings. We compare mechanisms where forum users rate individual posts and also mechanisms where the user is asked to perform a pairwise comparison and state which one is better.
The main metric used to evaluate a mechanism is the ranking accuracy vs the cost of reviews, where the cost is measured as the average number of reviews used per post. We show that for many reasonable probability models, there is no thumb (or star) based ranking mechanism that can produce approximately accurate rankings with bounded number of reviews per item.
On the other hand we provide a review mechanism based on pairwise comparisons which achieves approximate rankings with bounded cost. We have implemented a system, shoutvelocity, which is a twitter-like forum but items (i.e., tweets in Twitter) are rated by using comparisons. For each new item the user who posts the item is required to compare two previous entries.
This ensures that over a sequence of n posts, we get at least n comparisons requiring one review per item on average. Our mechanism uses this sequence of comparisons to obtain a ranking estimate. It ensures that every item is reviewed at least once and winning entries are reviewed more often to obtain better estimates of top items.