What Is Signaling, Really?

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.