Party dictates politics, which is why independants can play out in the big picture. If an independant runs the risk of taking away enough votes for a dem/rep to lose it for them, don't you think they (dems/reps) are going to look at the issues that independant is running and try to change their platform to pick up those voters?
Not saying the dem/rep who picks up the issue will do what they say, I can almost guarantee its a lie just to get votes. But the independant can be an influence to politics...