I am implementing a web application that has many users and I would give the users rating based on their activities and based on other users liking their activities. How would I implement such an algorithm for that? I am looking for elegant and smart algorithm that could help.
You are basically looking for Scoring Algos. These articles might help -
How not to sort by average rating
Rank hotness with Newtons law of Cooling
How Reddit Ranking Algorithms work
Hope this helps.