Assume the following problem: A popular website allows for users to either like or dislike its listed items (may it be movies, goods, people, or whatever). Each user may cast up to one like/dislike on any item she likes, but she has not to rate each and every item at display. (However, let us assume that each item has received at least one vote, i.e., ignore any items with neither like nor dislike.)
The website now likes to rank its items according to the given votes. Yet, it is quite clear that the two most trivial (and most frequently used) approaches do not yield meaningful results:
- If items are solely ranked by the total number of likes, the ranking disregards the number of dislikes.
- If items are ranked by the item's likes to dislikes ratio, the ranking ignores that items with many votes should have an edge over items with few votes. (An item with 199 likes and one dislike should end up better than an item with merely 2 likes and no dislikes.)
So my question is: How to do a sound (theoretically justifiably) ranking in the given scenario? I assume that concepts from statistical inference should be used, but I am not too familiar with that field so I don't know what concepts and models to choose.
Any help is appreciated. References to papers/publication addressing this ranking problem are also welcome.