Well, there's a little more to it than that. First off, there's the diffusion of responsibility. The more people there are that can make an invite, the more people assume somebody else would do it. Then there's the group dynamic factor. If anybody in the group has any issue with you, other people can feel awkward about inviting you. The last is the benefit factor. The benefit of getting more ingrained to the community for somebody who isn't established is for the person who isn't established. The people already ingrained have their routine, so their incentive to keep making overtures isn't nearly as strong as your desire for those overtures.