John Brockman's Edge site celebrates each New Year with a question, posed to a list of contributors. This year, the question is "What have you changed your mind about? Why?"
http://www.edge.org/q2008/q08_index.html
This essay is my answer to the question. The version posted on Edge is considerably shortened, to conform to the norms of the anthology. It also has a different title, the one used here being the generic title of the whole symposium.


When a politician changes his mind, he is a 'flip-flopper.' Politicians will do almost anything to disown the virtue – as some of us might see it – of flexibility. Margaret Thatcher said, "The lady is not for turning." Tony Blair said, "I don't have a reverse gear." Leading Democratic Presidential candidates, whose original decision to vote in favour of invading Iraq had been based on information believed in good faith but now known to be false, still stand by their earlier error for fear of the dread accusation: 'flip-flopper'. How very different is the world of science. Scientists actually gain kudos through changing their minds. If a scientist cannot come up with an example where he has changed his mind during his career, he feels the need to apologize. He is suspected of betraying the spirit of science. He is hidebound, rigid, inflexible, dogmatic! It is not really all that paradoxical, when you think about it, that prestige in politics and science should push in opposite directions. I'll take it no further than just to point it out, with a whiff of irony.

I have changed my mind, as it happens, about a highly paradoxical theory of prestige, in my own field of evolutionary biology. That theory is the Handicap Principle suggested by the Israeli zoologist Amotz Zahavi. I used to think it was nonsense, and I said so in my first book, The Selfish Gene. In the Second Edition I changed my mind, as the result of some brilliant theoretical modelling by my Oxford colleague Alan Grafen.

Zahavi's evolutionary theory of prestige was anticipated in the human sphere by the economist Thorstein Veblen. Anthropologists had drawn attention to 'Potlatch' ceremonies, whereby rival chieftains compete by means of conspicuous displays of ruinous generosity. You demonstrate your wealth and power by ostentatious donation or waste, culminating, in extreme cases, by setting fire to everything you possess. Veblen developed the idea in his concept of Conspicuous Consumption. Individuals consume goods not because they want them but in order to demonstrate status. Zahavi's version is evolutionary, and therefore assumed to be not consciously thought-out by its animal practitioners. But it comes to the same thing.

Zahavi originally proposed his Handicap Principle in the context of sexual advertisement by male animals to females. The long tail of a cock pheasant is a handicap. It endangers the male's own survival. Other theories of sexual selection reasoned - plausibly enough - that the long tail is favoured in spite of its being a handicap. Zahavi's maddeningly contrary suggestion was that females prefer long tailed males, not in spite of the handicap but precisely because of it. To use Zahavi's own preferred style of anthropomorphic whimsy, the male pheasant is saying to the female, "Look what a fine pheasant I must be, for I have survived in spite of lugging this incapacitating burden around behind me." For Zahavi, the handicap has to be a genuine one, authentically costly. A fake burden - the equivalent of the padded shoulder as counterfeit of physical strength - would be rumbled by the females. In Darwinian terms, natural selection would favour females who scorn padded males and choose instead males who demonstrate genuine physical strength in a costly, and therefore, unfakeable way. For Zahavi, cost is paramount. The male has to pay a genuine cost, or females would be selected to favour a rival male who does so.

Zahavi generalized his theory from sexual selection to all spheres in which animals communicate with one another. He himself studies Arabian Babblers, little brown birds of communal habit, who often 'altruistically' feed each other. Conventional 'selfish gene' theory would seek an explanation in terms of kin selection or reciprocation. Indeed, such explanations are usually right (I haven't changed my mind about that). But Zahavi noticed that the most generous babblers are the socially dominant individuals, and he interpreted this in handicap terms. Translating, as ever, from bird to human language, he put it into the mouth of a donor bird like this: "Look how superior I am to you, I can even afford to give you food." Similarly, some individuals act as 'sentinels', sitting conspicuously in a high tree and not feeding, watching for hawks and warning the rest of the flock who are therefore able to get on with feeding. Again eschewing kin selection and other manifestations of conventional selfish genery, Zahavi's explanation followed his own paradoxical logic: "Look what a great bird I am, I can afford to risk my life sitting high in a tree watching out for hawks, saving your miserable skins for you and allowing you to feed while I don't." What the sentinel pays out in personal cost he gains in social prestige, which translates into reproductive success. Natural selection favours conspicuous and costly generosity: favours handicaps because they are handicaps.

When Zahavi first explained the Handicap Principle to me, I voiced my scepticism with a reductio ad absurdum. Should we then expect, I demanded sarcastically, that natural selection will favour animals with only one leg and only one eye? Amotz's retort was witty enough, even then, to give me pause. "Some of our best generals," that former Israeli soldier reminded me, "have only one eye."

You can see why I was sceptical. It is all very well to pay a high cost to gain social prestige; maybe the raised prestige does indeed translate into Darwinian fitness; but the cost itself still has to be paid, and that will wipe out the fitness gain. Don't evade the issue by saying that the cost is only partial and will only partially wipe out the fitness gain. After all, won't a rival individual come along and out-compete you in the prestige stakes by paying a greater cost? And won't the cost therefore escalate until the point where it exactly wipes out the alleged fitness gain?

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 but will summarise the essence as a four stage argument. I'll use the convention that males are advertising to females, but it can be generalised to any cases where individuals are advertising to other individuals about anything.

1. Males really do vary in quality, and females really would benefit by choosing high quality males.

2. Each male is privy to some information about his own quality which is not directly available to anybody else. What is available to females is the advertisements that males choose to offer, which may or may not be truthful indications of their quality.

3. We can imagine all possible 'strategies' of advertisement that males might offer. For example one strategy might be complete honesty: perfect positive correlation between genuine quality and strength of advertisement. Another strategy might be the exact opposite: perfect dishonesty, or a negative correlation between quality and strength of advertisement. A third strategy might be a poker faced refusal to vouchsafe any information at all: zero correlation between quality and strength of advertisement. Mathematically, we can imagine all possible functions relating strength of advertisement to quality. Mathematically, we imagine a population of males adopting the full range of possible advertising strategies.

4. Females, exposed to male advertisements, also could adopt a wide range of strategies. One strategy might be total credulity: perfect positive correlation between strength of male advertisement and female preference. Another strategy might be the exact opposite: perfect negative correlation between strength of male advertisement and female preference. As with the male strategies, mathematically we imagine all possible functions relating strength of male advertisement to female responsiveness.

Grafen now set himself the task of discovering a pair of strategies, one male and one female, which were mutually stable, in Maynard Smith's sense of evolutionary stability ('ESS'). An evolutionarily stable male strategy is one such that, when all males adopt it, no male gains by doing anything different. An evolutionarily stable female strategy is one such that, when all females adopt it, no female gains by doing anything different. Grafen sought a pair of stable strategies, one stable within males and one stable within females, which remained stable in the presence of each other. He did indeed find such a mutual ESS and he was then able to examine its properties. They turned out to be thoroughly Zahavian! As follows:

1. At ESS, out of the whole range of possible display strategies, males will choose the honest strategy: correctly display your true quality, even if this betrays that your quality is poor.

2. At ESS, out of the whole range of credulity-incredulity strategies, females will chose the total credulity strategy: choose the male who advertises the highest quality.

3. At ESS, out of the full range of advertisements that males might choose, the advertisements that they actually will choose are costly. The advertising rule that is chosen at ESS is chosen precisely because it has the effect of lowering the fitness of the advertiser, all other things being equal.

4. At ESS, advertising is more costly to lower quality males. A given level of advertising strength damages a low quality male more than a high quality male. Low quality males incur a more serious risk from costly advertising than high quality males.

These ESS outcomes are full-bloodedly Zahavian. In a brilliant feat of theoretical biology, Alan Grafen has shown that we must all change our minds. I still find it quite worrying that we have to do so, because the idea seems so counter-intuitive. Of course Grafen has not shown that animal displays are always Zahavian. But he has shown that the main theoretical objection to the handicap principle was wrong. I should repeat, by the way, that my use of 'male' and 'female' was a convention for ease of exposition. You could go right through my explanation, substituting 'sentinel babbler' for male and 'feeding babbler' for female. Indeed, with a few adjustments to the explanation, you could go right back to humans and the advertising industry.

A word of caution, to end. Grafen's role in this story is of the utmost importance. Zahavi advanced a wildly paradoxical and implausible idea, which – as Grafen was able to show – eventually turned out to be right. We must not fall into the trap of thinking that therefore, the next time somebody comes up with a wildly paradoxical and implausible idea, that one too will turn out to be right. Most implausible ideas are implausible for a good reason. Zahavi eventually found his Grafen. Most proponents of wildly implausible ideas will not. Although I was wrong in my scepticism, and I have now changed my mind, I was still right to have been sceptical in the first place! We need our sceptics, and we need our Grafens to go to the trouble of proving them wrong.