Some good info here.
Ari, I completely understand your point. While I do tend to connect with people I don't know who have some shared interests, I am very discriminating with who I will allow to connect to my network. For example, maybe a couple times a month I get a request from someone who i may have connected with through a technology community group, asking to connect with one of my former business colleagues. Unless I know this person well, or something about their request is very compelling, i deny the connection. Why stay connected with these loosely connected people? For the reasons some others have mentioned here — I am happy to wade through the 50 bad requests to find the rare good request that I may not have otherwise found had my social circles been more closed off. I wish LinkedIn would add one feature: close connection vs loose connection, with the ability to assign different access levels. That, in my mind, would solve this issue of wanted to tap into the collective of an increasingly large social base, without budging on my standards for close connections.