I'd have to say that poly has made me think less in terms of "I" than I did before. I'm not more independent now. On the contrary, I have more responsibilities, more obligations. Every choice I make is going to affect more people. I can't behave as a free agent, and I don't think of myself as one. I'm a wife, a girlfriend, a lover, a friend, a sister, etc.
I really feel that poly is about building a family, not about having separate lives with separate people. I don't want to add anyone to our dynamic that can't relax in it. Potentials don't have to want sex or love or independent relationships with other people in the group, but they have to be able to spend time with our poly family as a group and be reasonably comfortable with situations where they aren't the center of attention. Group hangouts are the norm for people in relationships with me, and their partners are always invited.
Poly for me is knowing that I am not the center of everything. I am a part of something beautiful, but just a part. My sense of "we" is not a couple "we" but a family "we".