Here's my theory: I think the guy is probably a germ-o-phobe, and will only use a stall after it has been cleaned by the cleaning crew. In my building, you can tell when no one else has used a stall if the toilet water is pink (from the cleaning solution). So, when he gets to work in the morning or whatever, and sees that a stall hasn't been used yet, he wads up paper and places it in the door as a marker that that stall is still unused.
When he comes back later in the day, and sees the wad of paper on the floor, he knows that someone else has used that stall - that stall is now dead to him.
However, if he sees that his wad of paper is still in place, it means the stall is still unused, and he can safety use it without risk of infection. I think when he leaves that stall, he places another wad of paper to indicate that it's still useable, since as long as he's the only one that has used it since it was cleaned, it's still good. This would explain why some days there are multiple wads of paper on the ground by one stall - he's the only person to have used it all day.
What say ye?