Musing on identity|
I think I'm pretty solidly behind your ideas, beyond the first paragraph at the least. I don't see self-identity and imposed identity as necessarily relating. I think, personally speaking, that getting the identity imposed by others close to one's self-identity can be an excellent state of being (if you happen to like yourself, that is), but it is only in specific social circumstances that they interrelate.
A problem with the idea, in my opinion, is reducing the complexity of one's social interaction with the world into one thing - "Other". For I have my mother, who never seems to have a word of praise for me to my face but praises me to others, my potential significant other, who may see me as noble and lionhearted or as cowardly and vicious, my friends, my coworkers, and those people I run into every day who make their own judgments about me.
All of them have different opinions about who I am, and some of them have more impact than others. I would not say that that impact is easily defined as, say, one person believing I am dishonest pushes me further toward self-identifying as dishonest. Depending on the circumstances it may be true or at least compelling, or it may be a repulsive impression... and of course how one communicates their impressions vastly changes the way in which those impressions are interpreted.
I think self-identity and imposed identity are too complex, too disordered/random, occasionally to be defined in any simple equation. One simple experience as a child can significantly alter one's self-identity for, perhaps, life, and may not involve any predictable social interaction.