I do something similar to this, but instead of refusing to claim a political ideology, I simply observe my own recent behavior, inventory my own positions on the relevant issues, and ask myself, "From the outside, what part of the political spectrum does it look like I belong to?" This way I avoid identifying internally with any position.

Incidentally, in Social Security discussions and the like, people usually stop listening to me at around the part in the conversation where I mention that I believe that superintelligent machines will either destroy or save humanity before any of us reach retirement age.