It occurred to me that even if those points I made above are valid [regarding teasing etc], they don't explain why choosing the middle person changed in some communities from a purposeful act to a random act.

I think that this may have occurred because
1. the game was at one time a way of signaling to the community and your peers who you liked romantically [middle girl choosing boy and vice versa] Of course, this theory would hold true if these games were played by teens and young adults, the same population which played 'play party' songs.

and

2. the random selection may have helped to put a stop to favoritism that occurred when the person in the middle only selected those children who were the most popular. When you never know who is going to be picked and when, this puts all children on an equal footing...

I'd love to 'hear' your views on these theories.