"In general, online social networks had the smallest seed sets - 13 networks of this type had an average seed set size less than 2% of the population (these networks were all in Category A). We also noticed, that for most networks, there was a linear realtion between threshold value and seed size"
Though, for a company with direct access to their users via the UI, it would be a fairly trivial task to reach a significant subset. LinkedIn could reasonably push UI updates only to the target population. Given they have full access in the first place, I'm uncertain as to why they would want to engage in this form of marketing, though.