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the value proposition behind a business relationship is no different today than it was before LinkedIn - you have to provide value or at least perceived value (present or future). LinkedIn lowers the bar somewhat re how much value you need to add before someone agrees to establish a minimal business relationship (i don't have to hand enter stuff into my address book for example or file your business card). I think they have a long ways to go and could add much more value. we'll see. I frequently receive random connection requests and almost always decline unless the requestor can explain to me why they are making the request and why they think they can add value. But that doesn't really answer your question. As a company we use LinkedIn for recruiting/hiring/screening. LinkedIn generates the vast majority of their revenue via adding value to the recruiting/hiring process.
Of course I use it when I'm hiring, but aside from that, when I'm not dodging a daily flood of spam and refusing random connection requests (by people who will immediately follow with more spam)... I use it to investigate people during the early phase of a potential business relationship. It gives me a glimpse of their writing style. A look at the types and distributions of their network contacts tells me if they have been in their current industry for a long time, or if they are in transition to a new space. It tells me if they have a history of working on their own (independent decision maker), or if they have not personally wielded executive authority (learned the hard way by actual leadership). I can usually tell if they are a Faker (cut and pasted from others to craft the "perfect" profile), or a Maker (not perfect, but a real contributor and actually wrote their own profile).
I NEVER use it to market my own services in any way. I feel that's a breach of the "unwritten rules" which should govern an entrepreneurial resource.