First of all, regarding your top choice being more than four degrees away, how many confirmed first-degree contacts do you have in that system? 13? And who are they? Are any of them super-nodes, like Thomas Power, Joi Ito, or Reid Hoffman?

Just as the profile information is only as good as the metainformation people put in, so, too are the relationships. I have yet to actually be four degrees away from anyone -- often I discover that someone along the path is someone I already know, and just don't have a record of it in that system.

Furthermore, data collected by LinkedIn shows that four-degree introductions are successful more often than you would think, and three-degree introductions are frequently successful. I even have a story of a VC who got his current position at Ariadne Capital in London through a four-degree introduction -- trans-Atlantic, no less!
Trust is transferable, if it's actually communicated along the chain, and the intros aren't just passed along without personal comment.

Regarding "the artificial concept of degrees"...

People participate in this networks for different reasons. Those who are looking to increase their visibility and who are highly receptive to inquiries are perhaps better off in a more open environment like Ryze or Tribe. LinkedIn is better suited to those people who use their network more as a collaborative filter to make sure that only the interesting and worthwhile requests actually make it to them. The cost of that is slower communication, but sometimes it helps you get through to people who might be less accessible otherwise.

That's probably not a situation you yourself would often face as a Senior Editor at O'Reilly, which carries some weight, but for the typical person, stepping through those hoops may give them access to people who would be inaccessible to them directly.

Glad to see you're giving it some more time, though.

Scott Allen
Online Business Networks Blog