In The Great Gatsby, what kind of influence or power does Jordan Baker wield and what is her social position as it is depicted in the novel?
Jordan Baker wields little power but she has some influence. Her influence is vested in the fact that she is involved in a somewhat romantic relationship with the narrator, Nick Carraway. There is not much depth to it, but Nick does, in the end, express some regret for ending their acquaintance, as he states in chapter 9.
There was one thing to be done before I left, an awkward, unpleasant thing that perhaps had better have been let alone. But I wanted to leave things in order and not just trust that obliging and indifferent sea to sweep my refuse away. I saw Jordan Baker and talked over and around what had happened to us together, and what had happened afterward to me, and she lay perfectly still, listening, in a big chair...
For just a minute I wondered if I wasn’t making a mistake, then I thought it all over again quickly and got up to say good-bye.
Jordan then speaks:
....I thought you were rather an honest, straightforward person. I thought it was your secret pride.”
“I’m thirty,” I said. “I’m five years too old to lie to myself and call it honor.”
She didn’t answer. Angry, and half in love with her, and tremendously sorry, I turned away.
Jordan Baker is the person Jay Gatsby approaches to ask Nick to arrange a clandestine meeting with Daisy Buchanan at his house. It is Jay's dream to reunite with Daisy with whom he had an affair five years previously, before he went to war. Jay had spoken to Nick earlier and told him the following:
“I’m going to make a big request of you to-day,” he said, pocketing his souvenirs with satisfaction, “so I thought you ought to know something about me. I didn’t want you to think I was just some nobody. You see, I usually find myself among strangers because I drift here and there trying to forget the sad thing that happened to me.” He hesitated. “You’ll hear about it this afternoon.”
“No, this afternoon. I happened to find out that you’re taking Miss Baker to tea.”
“Do you mean you’re in love with Miss Baker?”
“No, old sport, I’m not. But Miss Baker has kindly consented to speak to you about this matter.”
Later that day, when Nick is with Jordan and she has informed him about Jay's request, he asks:
“Why didn’t he ask you to arrange a meeting?”
She then tells him that Jay wants to show Daisy his house and he is asking Nick to arrange the meeting since his house is next door.
Except for this arrangement and the fact that she is friends with the Buchanans and knows Jay Gatsby, as well as being involved with Nick, Jordan Baker has no power or influence. She does not intervene in the affairs of her friend, Daisy, or her husband, Tom. She plays the role of spectator. She gossips about such matters, but that is about all she does or is prepared to do. The request that she makes here is her only intervention for she feels that, "Daisy ought to have something in her life." The implication is, obviously, that Daisy is not quite happy since Tom has been gallivanting around having affairs and she, therefore, needs something to make her happy.
As far as her social status is concerned, Jordan comes from the same middle class neighborhood as Daisy. They became friends when they were still girls and Jordan witnessed Daisy's meeting with Jay when he was a young officer in service, just before he left to fight. Furthermore, her relationship with Daisy allows her to spend time with the very wealthy, a fact which probably suits her profile, for she is a professional golf player who regularly makes it into the newspapers. It is also clear that she regularly attends Jay's over-the-top extravaganzas at his home, where she met him and the two probably recognized each other.
The impression that one is left with is that Jordan is, on the whole, a spectator in the drama unfolding before her. Except for what she has done above, there is nothing more significant about her.