|The following is based on Van Buren and has not been confirmed by canon sources.|
This skill is the other half of what Speech encompassed. It is used for friendly diplomacy, subtle manipulation, and outright intimidation. Also, as previously discussed, I believe it could be used to good effect for attempting to control CNPCs (companion NPCs) during combat. Though CNPCs would be computer-controlled by default, I believe that giving the high-Persuasion character a chance to control their followers is sensible and good for the purposes of expanding Persuasion's usefulness throughout the game.
Some CNPCs are really agreeable, and some are belligerent jackasses who don't listen to anything. Some also go crazy when they see certain types of creatures or otherwise are annoyed by local behavior. A wounded CNPC can also be extremely difficult to control, as their life tends to take precedence over your desire to be a big winner. Persuasion can be used to offset a CNPC's tendencies to do exactly what they want, when they want. The higher the Persuasion, the more likely it is that the CNPC will allow the player to control them, even under duress.”— J.E. Sawyer