Every once in a while you receive "Can you endorse me?" inquiries in your LinkedIn Inbox. There is something which I do not like about such requests, if they come without recommendation for you first. It is like saying "I've worked with you long enough that you recognize value of the work I've done, which also means that I can do the same, but I do not really think that your contribution is worth my recommendation. Can you endorse me?" In fact, your recommendation of someone is the best request for endorsement. Indeed, why do you want an endorsement from person, whom you do not respect enough to give your own recommendation. It is not better than asking a stranger to sign a petition that you are the smartest person in this street.
And remember: the one, who cares most (about the other), gets most out of relationship.