I've noticed that most of the competitors on the show 'Cupcake Wars' mix their cupcake batter by hand, and not an electric mixer. Why is this?

Are you sure the ones you are seeing are maybe making vegan cupcakes? I have seen a couple of shows where they do mix vegan by hand. But mostly I have noticed them using mixers, so I'm not too sure is I am seeing the same thing as you.

I think the mixers are used mainly for the frosting, but it seems most (not all) use a large stainless steel bowl and a whisk to make the cake batter.