The most commonly used introduction to signaling, promoted both by Robin Hanson and in The Art of Strategy, starts with college degrees. Suppose, there are two kinds of people, smart people and stupid people; and suppose, with wild starry-eyed optimism, that the populace is split 50-50 between them. Smart people would add enough value to a company to be worth a $100,000 salary each year, but stupid people would only be worth $40,000. And employers, no matter how hard they try to come up with silly lateral-thinking interview questions like “How many ping-pong balls could fit in the Sistine Chapel?”, can't tell the difference between them.

Now suppose a certain college course, which costs $50,000, passes all smart people but flunks half the stupid people. A strategic employer might declare a policy of hiring (for a one year job; let's keep this model simple) graduates at $100,000 and non-graduates at $40,000.

Why? Consider the thought process of a smart person when deciding whether or not to take the course. She thinks “I am smart, so if I take the course, I will certainly pass. Then I will make an extra $60,000 at this job. So my costs are $50,000, and my benefits are $60,000. Sounds like a good deal.”

The stupid person, on the other hand, thinks: “As a stupid person, if I take the course, I have a 50% chance of passing and making $60,000 extra, and a 50% chance of failing and making $0 extra. My expected benefit is $30,000, but my expected cost is $50,000. I'll stay out of school and take the $40,000 salary for non-graduates.”

...assuming that stupid people all know they're stupid, and that they're all perfectly rational experts at game theory, to name two of several dubious premises here. Yet despite its flaws, this model does give some interesting results. For example, it suggests that rational employers will base decisions upon - and rational employees enroll in - college courses, even if those courses teach nothing of any value. So an investment bank might reject someone who had no college education, even while hiring someone who studied Art History, not known for its relevance to derivative trading.

We'll return to the specific example of education later, but for now it is more important to focus on the general definition that X signals Y if X is more likely to be true when Y is true than when Y is false. Amoral self-interested agents after the $60,000 salary bonus for intelligence, whether they are smart or stupid, will always say “Yes, I'm smart” if you ask them. So saying “I am smart” is not a signal of intelligence. Having a college degree is a signal of intelligence, because a smart person is more likely to get one than a stupid person.

Life frequently throws us into situations where we want to convince other people of something. If we are employees, we want to convince bosses we are skillful, honest, and hard-working. If we run the company, we want to convince customers we have superior products. If we are on the dating scene, we want to show potential mates that we are charming, funny, wealthy, interesting, you name it.

In some of these cases, mere assertion goes a long way. If I tell my employer at a job interview that I speak fluent Spanish, I'll probably get asked to talk to a Spanish-speaker at my job, will either succeed or fail, and if I fail will have a lot of questions to answer and probably get fired - or at the very least be in more trouble than if I'd just admitted I didn't speak Spanish to begin with. Here society and its system of reputational penalties help turn mere assertion into a credible signal: asserting I speak Spanish is costlier if I don't speak Spanish than if I do, and so is believable.

In other cases, mere assertion doesn't work. If I'm at a seedy bar looking for a one-night stand, I can tell a girl I'm totally a multimillionaire and feel relatively sure I won't be found out until after that one night - and so in this she would be naive to believe me, unless I did something only a real multimillionaire could, like give her an expensive diamond necklace.

How expensive a diamond necklace, exactly?  To absolutely prove I am a millionaire, only a million dollars worth of diamonds will do; $10,000 worth of diamonds could in theory come from anyone with at least $10,000. But in practice, people only care so much about impressing a girl at a seedy bar; if everyone cares about the same amount, the amount they'll spend on the signal depends mostly on their marginal utility of money, which in turn depends mostly on how much they have. Both a millionaire and a tenthousandaire can afford to buy $10,000 worth of diamonds, but only the millionaire can afford to buy $10,000 worth of diamonds on a whim. If in general people are only willing to spend 1% of their money on an impulse gift, then $10,000 is sufficient evidence that I am a millionaire.

But when the stakes are high, signals can get prohibitively costly. If a dozen millionaires are wooing Helen of Troy, the most beautiful woman in the world, and willing to spend arbitrarily much money on her - and if they all believe Helen will choose the richest among them - then if I only spend $10,000 on her I'll be outshone by a millionaire who spends the full million. Thus, if I want any chance with her at all, then even if I am genuinely the richest man around I might have to squander my entire fortune on diamonds.

This raises an important point: signaling can be really horrible. What if none of us are entirely sure how much Helen's other suitors have? It might be rational for all of us to spend everything we have on diamonds for her. Then twelve millionaires lose their fortunes, eleven of them for nothing. And this isn't some kind of wealth transfer - for all we know, Helen might not even like diamonds; maybe she locks them in her jewelry box after the wedding and never thinks about them again. It's about as economically productive as digging a big hole and throwing money into it.

If all twelve millionaires could get together beforehand and compare their wealth, and agree that only the wealthiest one would woo Helen, then they could all save their fortunes and the result would be exactly the same: Helen marries the wealthiest. If all twelve millionaires are remarkably trustworthy, maybe they can pull it off. But if any of them believe the others might lie about their wealth, or that one of the poorer men might covertly break their pact and woo Helen with gifts, then they've got to go through with the whole awful “everyone wastes everything they have on shiny rocks” ordeal.

Examples of destructive signaling are not limited to hypotheticals. Even if one does not believe Jared Diamond's hypothesis that Easter Island civilization collapsed after chieftains expended all of their resources trying to out-signal each other by building larger and larger stone heads, one can look at Nikolai Roussanov's study on how the dynamics of signaling games in US minority communities encourage conspicuous consumption and prevent members of those communities from investing in education and other important goods.

The Art of Strategy even advances the surprising hypothesis that corporate advertising can be a form of signaling. When a company advertises during the Super Bowl or some other high-visibility event, it costs a lot of money. To be able to afford the commercial, the company must be pretty wealthy; which in turn means it probably sells popular products and isn't going to collapse and leave its customers in the lurch. And to want to afford the commercial, the company must be pretty confident in its product: advertising that you should shop at Wal-Mart is more profitable if you shop at Wal-Mart, love it, and keep coming back than if you're likely to go to Wal-Mart, hate it, and leave without buying anything. This signaling, too, can become destructive: if every other company in your industry is buying Super Bowl commercials, then none of them have a comparative advantage and they're in exactly the same relative position as if none of them bought Super Bowl commercials - throwing money away just as in the diamond example.

Most of us cannot afford a Super Bowl commercial or a diamond necklace, and less people may build giant stone heads than during Easter Island's golden age, but a surprising amount of everyday life can be explained by signaling. For example, why did about 50% of readers get a mental flinch and an overpowering urge to correct me when I used “less” instead of “fewer” in the sentence above? According to Paul Fussell's “Guide Through The American Class System” (ht SIAI mailing list), nitpicky attention to good grammar, even when a sentence is perfectly clear without it, can be a way to signal education, and hence intelligence and probably social class. I would not dare to summarize Fussell's guide here, but it shattered my illusion that I mostly avoid thinking about class signals, and instead convinced me that pretty much everything I do from waking up in the morning to going to bed at night is a class signal. On flowers:

Anyone imagining that just any sort of flowers can be presented in the front of a house without status jeopardy would be wrong. Upper-middle-class flowers are rhododendrons, tiger lilies, amaryllis, columbine, clematis, and roses, except for bright-red ones. One way to learn which flowers are vulgar is to notice the varieties favored on Sunday-morning TV religious programs like Rex Humbard's or Robert Schuller's. There you will see primarily geraniums (red are lower than pink), poinsettias, and chrysanthemums, and you will know instantly, without even attending to the quality of the discourse, that you are looking at a high-prole setup. Other prole flowers include anything too vividly red, like red tulips. Declassed also are phlox, zinnias, salvia, gladioli, begonias, dahlias, fuchsias, and petunias. Members of the middle class will sometimes hope to mitigate the vulgarity of bright-red flowers by planting them in a rotting wheelbarrow or rowboat displayed on the front lawn, but seldom with success.

Seriously, read the essay.

In conclusion, a signal is a method of conveying information among not-necessarily-trustworthy parties by performing an action which is more likely or less costly if the information is true than if it is not true. Because signals are often costly, they can sometimes lead to a depressing waste of resources, but in other cases they may be the only way to believably convey important information.