In that situation with only 8-12 people you just need to pick up the phone and personally invite them. Will take all of an hour and you'll know the picture instantly, as well as make people feel wanted.

When I'm having a dinner party, or even a small party, I still call everyone personally. The difference it makes to getting people to come is enormous, it makes people feel wanted. Failing that, a personal email (rather than a batch send) also makes a big difference.

I agree that this works both ways - people are getting lazier at inviting people in the same way people are getting lazier at responding.