Right now sometimes people hold a drawing on Facebook (such as an item in the game Animal Crossing), with other users typing 1, 2, 3 and so forth to identify themselves, and the original poster could use a random number generator to get a number such as 25 to decide who the winner is.
But it can be chaotic when people happen to type in the same number at the same time, or when someone is typing 25 and the other person is still typing in 24. Also, some people then skip ahead, and type 28, and can make it more messy. Some people type 26, but by "replying to another user", so now there are two 26... and is not good either.
If the users are not asked to type in a number, but to type in "join" to join the drawing, it also is very difficult when the random number is 253, and now the OP has to count who user number 253 is.
Does Facebook or some 3rd party mechanism have a way to "choose a person" out of many? If Facebook has such a feature, then it should work in a way that is much more robust.