Tag Archives: signalling

Why rational agents may react negatively to honesty

Emotional people may of course dislike an honest person, just because his truthful opinion hurt their feelings. In contrast, rational agents’ payoff cannot decrease when they get additional information, so they always benefit from honest feedback. However, rational decision makers may still adjust their attitude to be more negative towards a person making truthful, informative statements. The reason is Bayesian updating about two dimensions: the honesty of the person and how much the person cares about the audience’s feelings. Both dimensions of belief positively affect attitude towards the person. His truthful statements increase rational listeners’ belief about his honesty, but may reduce belief in his tactfulness, which may shift rational agents’ opinions strongly enough in the negative direction to outweigh the benefit from honesty.

The relative effect of information about how much the person cares, compared to news about his honesty, is greater when the latter is relatively more certain. In the limit, if the audience is completely convinced that the person is honest (or certain of his dishonesty), then the belief about his honesty stays constant no matter what he does, and only the belief about tact moves. Then telling an unpleasant truth unambiguously worsens the audience’s attitude. Thus if a reasonably rational listener accuses a speaker of „brutal honesty” or tactlessness, then it signals that the listener is relatively convinced either that the speaker is a liar or that he is a trustworthy type. Therefore an accusation of tactlessness may be taken as an insult or a compliment, depending on one’s belief about the accuser’s belief about one’s honesty.

If tact takes effort, and the cost of this effort is lower for those who care about the audience’s emotions, then pleasant comments are an informative signal (in the Spence signalling sense) that the speaker cares about the feelings of others. In that case the inference that brutal honesty implies an uncaring nature is correct.

On the other hand, if the utility of rational agents only depends on the information content of statements, not directly on their positive or negative emotional tone, then the rational agents should not care about the tact of the speaker. In this case, there is neither a direct reason for the speaker to avoid unpleasant truths (out of altruism towards the audience), nor an indirect benefit from signalling tactfulness. Attitudes would only depend on one dimension of belief: the one about honesty. Then truthfulness cannot have a negative effect.

Higher order beliefs may still cause honesty to be interpreted negatively even when rational agents’ utility does not depend on the emotional content of statements. The rational listeners may believe that the speaker believes that the audience’s feelings would be hurt by negative comments (for example, the speaker puts positive probability on irrational listeners, or on their utility directly depending on the tone of the statements they hear), in which case tactless truthtelling still signals not caring about others’ emotions.

Claims that tickets are running out

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Both for paid and free events, the organisers often advertise that only a few tickets or places remain. The ad sometimes explicitly tells the viewer to register or buy now. Such advertising is costly, so there should be a benefit to the organiser. If the tickets have already sold out, then the benefit is zero, or at least smaller than if the event is not fully booked. The positive benefit from advertising a sold-out event is to build reputation for the future as an organiser of popular events, similarly to real estate agents putting a „Sold” sign in front of a house on which they closed the deal.

Given that the benefit of costly advertising is smaller when no tickets remain, some sellers should decide to advertise if and only if the event has not sold out. More generally, the probability of advertising should increase in the number of tickets remaining. In this case, rational buyers should treat advertisements saying that limited spaces remain as signals of the opposite – frequent ads show a desperate seller facing low demand. If most buyers think this way, then such advertising is counterproductive, because buyers want to delay their purchases when the probability of being able to buy in the future is large enough. The option value of waiting comes from the possibility that the buyer’s preferences change – a better event may become available, or some emergency may prevent the buyer from attending. Getting a refund for a ticket already bought is at least a hassle and may even be impossible.

The widespread claims of limited space remaining suggest that these ads boost purchases. One reason may be buyer attention – ads make them notice the opportunity to buy, which some of them wish to take advantage of. However, any ads draw attention to the event, so raising awareness cannot be the reason for the specific claim that tickets are running out.

For most events, buyers do not want to coordinate with the largest possible crowd, only with their friends, so do not prefer a fully booked event to a half-full one. Thus claims that the event is almost sold out are difficult to explain by the seller trying to coordinate buyer actions.

Some irrationality of buyers or the seller seems necessary to explain messages that demand is low. Either the buyers take the claim literally instead of using Bayes’ rule to infer the opposite, or the seller advertises despite ads decreasing demand.

It is an empirical question whether the target audience of ads saying that space is running out interprets these as signalling high or low demand, and whether these messages make people delay their purchase or speed it up.

Mugs, pens and USB sticks as advertisements

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Several universities I have visited give free mugs to seminar speakers as advertisements for themselves. Similar branded objects (pens, USB sticks, T-shirts, baseball caps) are handed out by firms and political campaigns as part of their marketing.

The idea of giving people practical objects instead of flyers, junk mail or banners is to make the recipients use these objects (as opposed to throwing these away or storing them at the back of a closet), preferably in a public setting, and thus increase the visibility of the advertiser. For this, the more usable the handout, the better.

Unfortunately, the people ordering these objects in bulk and paying for the brand logo to be printed on these are busy administrators who do not connect the overall purpose the marketing campaign to the properties of the objects. Specifically, the mugs should have a large handle that lets more than two fingers hold it, the mug should be short with a wide mouth for easy filling and washing, and should not be too fragile.

Pens should write well and be ergonomical, not angular or too narrow. I have seen branded pens violating all these suggestions. For example, the Australian National University pens are of flimsy plastic, create ink splotches and the ink runs out quickly.

The USB sticks handed out by the University of Queensland had a metal cover which increased the USB drive’s bulk and scratchiness. Also, the USB was wide and thick, making it impossible to plug in side by side with another USB. The small capacity of the USB was also behind the times.

To advertise with an object, it would make sense to print the advertiser’s name and other relevant information in large readable font on the object. The logo is not useful unless it is already widely known by the target audience and associated with the advertiser. The readability suggestion is violated by the Singapore Management University’s mug, which has SMU written on it in complicated calligraphic script that is difficult to decipher even for someone who knows what the abbreviation SMU means.

For people to develop a positive view of the advertiser, the object should not seem too cheap or bad quality. By contrast, most free T-shirts are the cheapest ones that could be bought wholesale, made of the most threadbare and transparent cotton, which discourages their use.

Formal clothing is a bad equilibrium of a coordination game

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What clothing happens to be considered formal is an equilibrium of a coordination game: if most others think that a given clothing item is formal, then a person who wants to be seen as formally dressed is better off choosing that garment. If enough people who aim to dress formally choose certain clothing items, then those garments will be interpreted as formal. Different cultures and eras have considered different clothes formal, e.g. tights for men were formal in Europe during Napoleonic times, but are not now.

Current formal clothing is a bad equilibrium because suits and shirts are difficult to clean, labour-intensive to iron or press, and restrict movement. A better equilibrium would be to interpret as formal some garments that are comfortable, environmentally friendly, easy to care for and cheap. It is unfortunately difficult to change equilibria in a society-wide coordination game, because a majority of people would have to change their beliefs in a short time.

The reason why suits are seen as formal is historical: these were fashionable at the height of the British Empire, which was the richest and the most powerful country in the 19th century, thus a trendsetter in the first era of globalisation. British fashion was copied in North America and Europe, spreading to the colonies from there. Labour-intensive clothes were a way for Victorian nobility to signal wealth, because only the rich could afford to hire enough servants to make and care for their clothes. In many cultures, wearing impractical clothes (toga, long dress restricting leg movemen) has been a way to signal that one does not have to work. Similar signals of leisure were pale skin (because most work was outdoors), soft clean hands (because most work was manual and dirty), straight posture (because work often involved stooping). More extreme signals of leisure were physical changes that made most jobs of that era and region difficult or impossible: women’s foot-binding in East Asia, mandarins’ long fingernails in China.

Contrary to pale skin demonstrating leisure in Victorian Britain, in modern developed countries, a suntan is a signal of wealth, because most work is indoors and most trips to tropical places or simply outdoors are costly and time-consuming vacations. A similar reversal of the meaning of a signal is that a fat belly showed wealth when food was scarce, but in modern developed countries with an obesity epidemic, developing an athletic physique takes time and effort, so being fat is statistical evidence of poverty.

Signals of wealth have always invited cheaper imitations. For example, solariums provide suntanning cheaper than travel to the tropics. Slimness can be faked with liposuction, a corset or less drastically with a tailored waist and vertical stripes that are closer together or narrower at the waist area. The appearance of broad shoulders is achievable by wearing a suit jacket with padded shoulders.

One reason for why a business suit looks the way it does is to make the man wearing it appear taller, slimmer in the waist, and broader-shouldered, thus more masculine and attractive. The V-shape formed by the lapels uses the well-known visual perception error that an object at the open end of a V looks larger than an identical object at the tip of the V. The front of a suit jacket thus creates the appearance of a slim-bellied, muscular man. If the wearer’s belly allows, then a suit jacket usually also has a tailored waist, which further visually narrows the middle of the body. The vertical lines created by the tie and the creases of the pants make the wearer look taller and slimmer, which is often accentuated by vertical stripes on the suit. It is very rare to see a suit with horizontal stripes.

The visual illusion of attractiveness that a suit creates provides a extra incentive to stay in the equilibrium in which suits are considered formal clothing. To ease the transition to a new equilibrium in which the clothes perceived as formal are more practical, the new formal clothes should improve the wearer’s looks even more than a suit. This is not difficult, because many garments may have V-shaped patterns printed on the upper body, vertical stripes on the lower, have a tailored waist and shoulder pads. The patterns and cut may be designed based on psychology research to maximise the athletic appearance of the wearer. Anything achieved with a suit may be replicated and further optical enhancements added, for example printed outlines of muscles and puffed upper sleeves.

Signs with strong language are not enforced

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Various prohibiting signs are posted in many places, saying for example “No smoking”, “No trespassing”, “No skateboarding”, etc. The language of a sign with the same message can be stronger or weaker, e.g. “Smoking prohibited” vs “No smoking. Strictly enforced” or “Trespassing forbidden” vs “Strictly no trespassing. Violators will be prosecuted to the fullest extent of the law.” It seems that there is a negative correlation between the strength of the language and the strength of enforcement. The rules stated on signs threatening strict enforcement or prosecution seem not enforced at all. Non-enforcement is certainly the case for the “Smoke-free campus. Strictly no smoking” signs around the Australian National University and for similar signs around other universities that I have visited.
Why might stronger language of the sign indicate non-enforcement? Stronger language is also longer, requiring a larger sign and more paint, which makes signs with stronger language slightly more expensive to put up. So why pay more for signs that suggest non-enforcement?
Local people learn the rules and their actual level of enforcement over time. For them, signs are not really necessary. Therefore, signs are put up only for first-time visitors or for legal reasons. Legalities usually just require some legible sign, not a long and strongly worded one, so to satisfy the law, the optimal choice is a shorter and simpler text that fits on a smaller, cheaper sign.
First-time visitors are either uncertain about the enforcement level or know it. If they know, then they are effectively locals – for them, there is no need for a long sign. If the visitors are uncertain, then they might infer the enforcement level from the strength of the language. This can go two ways. If the visitors are rational and the strength of the language is negatively correlated with the level of enforcement, then a shorter sign signals stronger enforcement and deters rule-breaking better. Then all signs would optimally be short. If the visitors are irrational and interpret the signs literally, then more strongly worded signs deter rule-breaking more. The negative correlation between strong language and enforcement suggests that people are irrational and take threats literally. Or that those putting up signs are irrational and for some reason choose the less effective strongly worded signs.
An alternative explanation is countersignalling (Feltovich, Harbaugh and To 2002). In this model, there are three types of sign-posters. The first type does not care much about whether the text of the sign is obeyed (may post the sign only for legal reasons). The second type cares a little bit, but not enough to pay for much enforcement. Still, the second type slightly enforces, so there is a small positive probability of some kind of punishment when breaking the rules. The third type really wants the rules to be followed and invests in enforcement correspondingly. The potential rule-breakers quickly learn from punishments whether they are dealing with the third type. So the third type does not need any particular kind of signs to distinguish himself from the first two.
The first two types are harder to tell apart. The first type is not interested in distinguishing himself from the others – in fact, being confused with the others is beneficial, because it is more likely to make people obey the rules. The second type would like to distinguish himself from the first type and be confused with the third type, but this desire is not strong enough to pay the same enforcement cost as the third. So the second type will settle for distinguishing himself from the first type. This is done by paying for slightly larger signs with stronger, longer language on them. In this case, in the absence of experienced enforcement, the potential rule-breakers respond more to strongly worded signs than to short ones.
For an external observer, it is difficult to distinguish a small amount of enforcement from none, so the perception arises that enforcement goes together with short signs, but non-enforcement sometimes with long, strongly worded signs and sometimes with short signs. So there is a negative correlation between the strength of enforcement and the strength of the language. This correlation is stronger if the fraction of the first type in the population of sign-posters is small, for example because some first types do not post signs at all. People posting signs are a selected sample from the population of those who want some rule obeyed. The selection oversamples those who care more.

On accepting apologies

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There seems to be a social convention that an apology has to be accepted and that someone who does not is unfriendly and a bad person. This seems strange to me, because an apology often tries to undo deeds with words, or cancel unthinking words with considered ones.

The willingness of most people to trade words for deeds seems irrational to me – there is a qualitative difference between words and deeds, in that words can be neutralized within the hearer’s mind. If the hearer or reader does not understand, hear or attach emotional significance to words, then these have no effect. Deeds, on the other hand, have consequences that are not just in people’s heads. A punch causes bruising even if imagined to be a caress. An insult does not cause bad feelings if it is interpreted as a joke by all concerned.

Accepting words in compensation for deeds makes one manipulable. The perpetrator of bad actions can get away with them repeatedly by promising each time to change and to sin no more (Hitler’s “last territorial demand”). The social convention that words have to be accepted as compensation helps the unscrupulous. If instead good works in sufficient quantity were required to make up for misdeeds, then taking advantage of others would be less profitable. Some people would have to spend a lifetime undoing their crimes, which creates the incentive problem of how to make criminals work. Perhaps gradually easing ostracism and restrictions as the debt is worked off. The quantity of good actions required must be large enough to make the overall profit from a bad deed negative.

Cancelling unthinking words with a considered apology benefits impulsive liars who initially insult and then talk their way out of the opprobrium by pretending to be sorry. Every time I find in the media that a politician or a white collar criminal says sorry, I interpret it as them being sorry they were caught. If they were sorry about the deed itself, they wouldn’t have done it in the first place.

A good person who did something bad by accident would volunteer to make amends. They would not have to be forced to it as punishment. Of course, if volunteering to compensate starts being interpreted favourably enough by society, then selfish and manipulative people would also volunteer. Making amends is a costly signal of good intentions, but if the benefit of signalling is large enough, then even the bad types signal to imitate the good.

Signalling by encouraging good decisionmaking

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Con artists pressure people into quick decisions. Marketing mentions that the offer is for a limited time only, so buy now, no time to read the small print. Date rapists try to get victims drunk or drugged. In all these cases, the goal is to prevent careful reasoning about what is happening and the decisions to be made. Also to prevent the victim from consulting others. Being pressured, confused or bullied while deciding is a danger sign, so one way for honest sellers to distinguish themselves is by encouraging good decisionmaking. Giving people time, referring them to neutral sources of info, asking them to think things over before deciding are all ways to make decisions more accurate.
More accurate decisions distinguish between good and bad deals better, which benefits honest sellers and harms con artists. This differential effect of information on good and bad types enables signalling by precision of information, where good types want to reveal as much as possible and bad types want to obfuscate. Information unravelling results – the best type has an incentive to reveal itself, then the second best type, then the third best etc. By not revealing, one is pooled with the average of the remaining types. In the end, the only type who does not strictly prefer to reveal itself is the worst type.

Sexual signals are similar to money

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Ronald Fisher analyzed signalling in biology through traits that do not confer direct fitness advantage (higher survival or fecundity), but are desired by the opposite sex. This attraction is an equilibrium in a coordination game – if a potential mate has traits desired by the opposite sex, then the offspring with that mate are likely to have these traits as well and succeed in attracting the opposite sex. The traits confer a mating advantage, which is part of a fitness advantage, justifying the desirability of the traits.
It is a coordination game, because in a different equilibrium, traits without a direct fitness advantage are not desired. Then these traits do not give a mating advantage to the offspring and therefore do not have an indirect fitness advantage either. Then it is not fitness-enhancing to desire them. In summary, if a trait is expected to be desirable in the future, then it is desirable now, and if a trait is expected to be neutral or undesirable, then it is neutral or undesirable now.
Fiat money is inherently worthless, but in one equilibrium of the money game, has positive value in terms of other goods. If everyone expects that others will accept money in return for goods in the future, then it is useful to obtain money now. So everyone is happy to deliver goods in return for (a sufficient sum of) money now. The money game is a coordination game, because if everyone expects money not to be accepted in the future, then they do not give goods for money now. If money is expected to be worthless, then it is worthless, and if money is expected to be valuable, then it is valuable.
An overview of signalling in biology is at http://en.wikipedia.org/wiki/Signalling_theory and Fisher’s theory at http://en.wikipedia.org/wiki/Fisherian_runaway
The coordination game of money is studied by Kiyotaki and Wright (1989, 1993): http://www.jstor.org/stable/1832197 http://www.jstor.org/stable/2117496 and more simply explained in van der Lecq “Money, coordination and prices” https://books.google.com.au/books?id=r1r40SB0Wn8C&pg=PA29&lpg=PA29&dq=fiat+money+coordination&source=bl&ots=iI0M96m-qz&sig=lRHBAWIXYZs2V5S-iNFeH-2yar8&hl=et&sa=X&ei=d3lqVeneJ8TvmAX4vIGgDg&ved=0CEoQ6AEwBw#v=onepage&q=fiat%20money%20coordination&f=false