>in Sparta they did it by shouting (loudest won — which the Athenians thought very weird)
I don't know why the Athenians thought this to be weird, I guess they had their reasons. But I can think of one benefit of the Spartanian way.
If you raise hands, you can quickly change when you see what others are doing. When you shout, you have to inhale as much as you can to shout as loud as you can. You first have to make up your mind, before you can hear others.