Lenny Zeltser received some very good answers as to why there are fewer scams on LinkedIn than Facebook.
I think this is the best answer:
People’s LinkedIn interactions have a professional perspective. This frame of mind doesn’t generate the same social/emotional response as Facebook, which makes them more resistant to being tricked, suggested @adamshostack. In addition, @marypcbuk pointed out that people tend to pay more attention to their LinkedIn interactions, because they police their professional activities more carefully than personal ones.
Facebook interactions are much more free flowing and emotional while LinkedIn, being professionally oriented, interactions are more thoughtful. On LinkedIn people are more cautious because they are more concerned with their reputations.
The other answers definitely have merit as well.