The boy should go before the girl. AND THE GIRL SHOULD HAVE NO IDEA THE BOY IS LOOKING INTO HER!! This way, the girl should only know when a boy says yes, and it is only the boys who need to deal with rejection (since the girl will only have the opportunity to decide yes or no after the boy says yes).
The problem is that people spill the beans (see previous thread titled “privacy” for further discussion). But ideally, the way it should work is that a girl will not know when a boy has said no.