How do I win over a stubborn girl?

Pretty simple, I like this girl but she's so incredibly stubborn and won't go out with 'just anybody'. I'm also her ex but we broke up over stupid reasons, she has said that she's open to getting back together but only when it's because we both want to, she respects me enough to not use me which I'm quite glad about.

Anyway I want her back, she's said before that she wants another chance to come natural if it's in both of our best interests, but even then she falls for all the 'big godlike assholes' around so easily it's like picking up a kettle.

Ideas?
How do I win over a stubborn girl?
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