In the first edition, I wrote, "I don't believe in this theory, although I'm not nearly as confident in the validity of my skepticism as I was when I first heard about it." I'm glad I wrote "although," because Zahavi's theory now seems far more plausible to me than it did when I first expressed that opinion. Several respected theorists have recently begun to take it seriously, including my colleague Alan Grafen, who, as has been noted in print, "has the rather annoying quality of always being right." He has constructed a mathematical model based on Zahavi's statements and claims that it works. And that this is not some fantastical, esoteric parody of Zahavi, like those others have toyed with, but a direct mathematical embodiment of Zahavi's idea. I will consider here Grafen's original ESS model, although he himself is currently working on a full genetic version that should surpass the ESS model in some respects. This does not mean that the ESS model is actually wrong. It is a good approximation, as are essentially all ESS models, including those described in this book.
The handicap principle is potentially applicable to all situations in which individuals attempt to judge the quality of other individuals, but we will limit our consideration to males advertising themselves to females. This situation is chosen for the sake of clarity. Grafen notes that there are at least four approaches to the handicap principle. They can be called the following: 1) qualifying handicap (any male that survives despite his handicap obviously possesses otherwise excellent qualities, so females choose him); 2) revealing handicap (males perform some difficult task to reveal their hidden talents); 3) conditional handicap (only high-quality males develop a handicap); And finally, 4) Grafen's favorite interpretation, which he called the strategic choice handicap (males possess private information about their own qualities, not shared with females, which they use to "decide" whether to develop a given handicap and how significant it should be). Grafen's strategic choice handicap is amenable to analysis using the ESS. It is not based on the prior assumption that the advertising used by males will be expensive or create handicaps. On the contrary, males are free to develop any type of advertising: honest or deceptive, expensive or cheap. But Grafen shows that, given such freedom of choice at the outset, the handicap system may well prove stable.
Grafen proceeded from the following four assumptions. First, males differ in quality. But quality is not some snobbish notion, like frivolous pride in one's old college or fraternity. (I once received a letter from a reader who concluded, "I hope you won't find my letter presumptuous, after all, I am a Balliol alumnus.") Quality, for Grafen, means that there are good and bad males, in the sense that females will benefit genetically if they choose good males as mates and avoid bad ones. "Good" means strong muscles, capable of running fast, finding prey, and building strong nests. We are not talking about the ultimate reproductive success of a male, since this depends on whether a female chooses a given male. Discussing this now would distract us from the core of the matter. It may or may not manifest itself in the model.
Secondly, females cannot directly assess a male's quality and must rely on his advertising. At this stage, we make no assumptions about the honesty of this advertising. Honesty is something else entirely; it may or may not be detected in the modeling, but that's what the model is for. A male might, for example, "grow" padded shoulders to create the illusion of greater size and strength. The model should show us whether such a false signal will be evolutionarily stable or whether natural selection will favor modest, honest, and truthful advertisements.
Third, males, unlike the females who examine them, in a sense "know" their quality and adopt a specific advertising "strategy"—a rule of conditional advertising depending on their quality. As usual, by "know," I don't mean consciously knowing. Males are assumed to have genes that are activated depending on the male's quality (there is reason to believe that this information is not publicly available, since a male's genes are embedded in his biochemistry, meaning that, by their position, they are undoubtedly much more responsive to his quality than a female's genes). Different males choose different rules. For example, one male might follow the rule: "I display a tail whose size is proportional to my true quality." Another might follow the exact opposite rule. This allows natural selection to adjust the rules, favoring males who are genetically programmed to apply different rules. The level of advertising need not be directly proportional to true quality. A male could even choose the opposite rule. We only require that males be programmed to apply some rule to determine their true quality and choose a particular level of advertising based on this (for example, tail or horn size). As for which of the possible rules will ultimately prove stable, this is again one of the problems the model should help solve.
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