Let's assume that the user both wants to connect to as much of the network as possible and they also want to use their local connection bandwidth as efficiently as possible. The assumption is that where there are messages there are clients thus as you try to receive as many messages as possible you are also increasing the number of hosts you will reach. It also makes the assumption that where there are clients there is content. These two goals are not mutually exclusive but they are interrelated goals and it is not likely that you can achieve both to their full extent at the same time. There is some insight available if we turn to the classical information retrieval literature.
Precision is the percentage of hits in a search that are about the desired resource.
Recall is the percentage of the available desired resources that were returned as hits in the search. Thus one can think of another Venn diagram in which we have the results returned by a search as one set and the desired resources as another search. The more than that the search results overlap with the desired resources the better the search engine is. Also one can think of precision and recall as simply conditional probabilities in terms of the result set and the desired resources set. Recall and precision in terms of conditional probabilities.