I have read the factiod several times (usually in women's magazines) that the cleanest stall in public restrooms is the first one, because it is the least used. This is due partly to the fact that people feel they have more privacy the further they are from the door.
I am not sure how men do it, but most women are very concerned with restroom cleanliness -- resorting to hovering, covering the seat in tissue paper or just holdinging it. Becuase of this, I believe that many women, after learning of this factiod, will begin choosing the first stall.
And here in lies the problem. As people learn the first stall is the cleanest because of it's under use, and then begin to use it, this will begin to make it the most used and in turn the dirtiest -- thereby making this factiod no longer true.