Verbal arguments of this kind can take us only so far. Mathematical models are needed, and various people supplied them, notably John Maynard Smith who concluded that Zahavi's idea, though interesting, just wouldn't work. Or, to be more precise, Maynard Smith couldn't find a mathematical model that led to the conclusion that Zahavi's theory might work. He left open the possibility that somebody else might come along later with a better model. That is exactly what Alan Grafen did, and now we all have to change our minds. I translated Grafen's mathematical model back into words, in the Second Edition of The Selfish Gene (pp 309-313), and I shall not repeat myself here. In one sentence, Grafen found an evolutionarily stable combination of male advertising strategy and female credulity strategy that turned out to be unmistakeably Zahavian. I was wrong to dismiss Zahavi, and so were a lot of other people.