Your Reputation is subject to change depending on a varity of issues, such as not completing a misson, abandoning a mission and even doing missions for the other unafilliated brokers. The influence you earn is the broker's passing on how good a job you are doing vs the skill level you accept. As an Elite, if you only accept missions rated for a harmless for example, you'll notice that your rep will develope a red or blue triangle point either up or downward. It take two to three mission to get the arrow point up wards, two or three more to change from red to blue downward, two to three more to get it upward and finally two or three more to elimiate it. Before any more rep will be applied to the graph. If and when the graph is free of either the red or blue triangles does any influence you may earn sent to the majors. Though I do belive it is simular to earning rank after you have reached 100 percent. Where as you are still progressing to the next level but can't see it. Thus sometimes it would seem that you didn't do much and got a big bump and other times worked your butt off and only got a small bump up.
Basically, complete any and all missions on time, if your working on the major rank, don't do anything in regards to the brokers whom are not affiliated with the major rank your trying to achieve. Any and all money donated goes either directly to the major or via the broker in the form of influnce. Call it what you will, but it all goes to the major ranking in the long run.
I believe the positive work you do accumulates just like when the major graph is at 100% and you can't see any progress. If you have ever noticed, that immediately after becoming allied, your major ranking gets a nice bump and then slows down to a turtle again almost immediatly afterward.
Alway have rebuy and when ranking for the major's never accept non affilliated broker, regardless of reward. Yes, it's tempting, don't do it. The added missions to get rid of those dam triangles are a pain in the asss. Which is a true statement remembering that you sitting there longer to do them because you make the aflilleated broker angry.