This question is really telling about the type of GM who is running the game. Should a player's character be able to over-ride other player's choices by using a "social" skill in-character? Should a player's character's social skills inform other players as to the level of persuasiveness or an argument?
I would say No and No, to each of these questions.
To the first question: I am in the camp that believes that, short of supernatural intervention, a the character's player is in control of that character's choices. It's bad enough getting players to go along with scenarios that involve them getting captured or losing any sort of physical control over their character's destiny. Say the party captures a baddie and the everyone in the party says that the prisoner should be tortured except for my character. As a player, I would probably flip out if I was in a game, playing pacifist-type who was protecting a prisoner and another player rolled a persuade skill and the GM had my character go along with, or even happily step aside from the situation. This is because it is important to me that my character to be presented in the story as I intend. Which leads me to my next question!
So, if a player makes their social skill roll and gets a high result, but the player is essentially saying "Go, hit thing with rock! Make it smash!" can the GM turn to the players and say "So-and-So makes a good argument to make smash with rocks." The opposite of this is if a player makes an argument that would make Daniel Webster weep somberly, and then completely fluffs his roll, does the GM turn to the players and say "So-and-So sounds like a jerk and you hate his face for what he just said." (After all, a lot of games impose negative reactions on badly failed reaction/influence rolls.) Neither of these scenarios really would sit well with me. There's also the argument that a highly persuasive character on paper, with a dunce player, (just like a highly intelligent character, or a lawyer with high law skills) is supposed to have a character with the ability to make highly persuasive arguments. Well, this is true, the character's skills allow them to have a great effect in the context of the game, on the NPCs. This way a lot of abstraction can be had to keep things flowing. I, personally, do not want to sit down and have a GM role-play out a character persuading 40 people, in real time, with another player. Have you watched a town hall on CNN? I shudder thinking about it. So, yes, the dunce player, with the highly intelligent, persuasive super-lawyer can make amazing arguments and defenses as described by the GM and as they effect the NPCs and story accordingly... NOT the other players' characters (unless a player decides to change their character's mind.)
So says me.
And, who thinks the next episode of BearSwarm is going to cover social skills affecting players? Hands?