It’s a bit early to start writing the definitive Google Plus SEO Guide, but I think the above screenshot says all you need to know.
When I am signed in, page one of searches for my name are dominated by my blog, my G+ profile and four of my recent G+ posts. When I am not signed in, I get only my G+ profile link in the middle of page one.
What does this mean? SERPs for signed in users connected to other + users can be heavily influenced by G+ posts.