Everyone I have asked argues two reasons to reject LinkedIn invitations.
The first one is because they think LinkedIn "connections" represent "relationships"; "if I "link" with you I telling the world that person has a profesional or academic relationship with me".
But have a look to your list of "connections" for a minute. Are you sure all those "connections" represent business or school real relationships? If you have more than 150 (Dunbar's number) you'll have a hard time to justify it. Are you sure that in your connections there is no any ex-colleague and/or ex-client that you linked even if you didn't want to? Be honest, you haven't spoke with most of your connections for months and in many cases that "relationship" is just you both worked for the same company or attended the same class at the university.
So, if you LinkedIn connections are already so weak, why would you reject a LinkedIn connection invitation?
Here is where the second reason appears. "I don't know that person". But my point is, if a person has any interest in "connect" with you how does it matter that you don't know her? Is it really clever to reject the invitation?
I think the failure rest in people assigning a value to LinkedIn "connections" that they don't really have. You think your "connections" define you and the more important your "contacts" are the more valuable you look as a profesional. But that's not true. Even if it is true for you it won't be true for an external observer, the one that is looking at your LinkedIn profile. Everybody knows the contacts that are really important are those that will answer your phone call immediately and that's not reflected in LindeIn.
But even if that were true, even if LinkedIn connections had that value, rejecting a "link" invitation would mean that you think that person does not have a chance to become important to you in the future and that means that you are beeing arrogant today and might be proven wrong tomorrow...
Javier Arias González