I listened to an episode of the Happy Jacks RPG Podcast when they talked about how to convince another PC, while still keeping that free will. I liked the idea voiced there and decided to put it up here for keeping.
When you want to persuade another PC, make you roll for whatever ability or skill you use. If you succeed, now ask the player of that character what they might be convinced by, and what buttons pressed might give them the idea to change their minds. Now role play out the scene, with that newly gained knowledge from the meta level.
You might not convince them in the end, but you gained something from having a character that was more socially experienced or convincing than you are. Also, nobody was robbed of their free will be a roll of a die.
I might work out.