I've written previously on some of my strategies on dealing with the plethora of LinkedIn invitations I seem to get; trust me on this I'm too lazy today to provide links to previous articles.
I live and work in metro Detroit, and get a lot of connection invitations from Detroiters that I just don't know. I send a reply that goes something like this:
"Thank you for the invitation. My rule for Detroit area people I don't know is that I need to know them before I accept. If you'd like, we can meet for lunch, breakfast, or coffee to get to know each other first."
Funny thing is, I usually don't hear anything back on that reply.
Part of what I think is going on is a change to LinkedIn's "People You May Know" page. It shows you a bunch of people you may know, and there is a link that says "Connect" - hit it and the default "I'd like to add you to my professional network." message comes up. The sender doesn't bother to personalize it (big mistake in my book) and then seem to be surprised that it isn't automatically accepted.
This is just unfortunate. I've developed some great relationships from this rule, and developed other relationships as a result.
So am I bothered that I'm usually not getting replies. Yeah, but not too much. If they can't bother with a reply I'm better off not accepting.