The night before the Billboard Music Awards in Las Vegas in May, Madonna was sitting in the arena attached to the MGM Grand hotel, staring at a double of herself. The double, who was standing on the stage many yards away, was younger and looked Asian but wore a similar lace minidress and a wig in Madonna’s current hairstyle, a ’30s movie star’s crimped blond waves. “It’s always the second person with the wig — she wants to see it,” a stage designer said, adding that when she makes a decision, she is definitive. “Madonna wants 10 options, but when she says it’s the one, it’s the one.”