The rise of the social media sites, such as blogs, wikis, Digg and Flickr among others, underscores the transformation of the Web to a participatory medium in which users are collaboratively creating, evaluating and distributing information. The innovations introduced by social media has lead to a new paradigm for interacting with information, what we call 'social information processing'. In this paper, we study how social news aggregator Digg exploits social information processing to solve the problems of document recommendation and rating. First, we show, by tracking stories over time, that social networks play an important role in document recommendation. The second contribution of this paper consists of two mathematical models. The first model describes how collaborative rating and promotion of stories emerges from the independent decisions made by many users. The second model describes how a user's influence, the number of promoted stories and the user's social network, changes in time. We find qualitative agreement between predictions of the model and user data gathered from Digg.