Tag Archives: signalling

Dilution effect explained by signalling

Signalling confidence in one’s arguments explains the dilution effect in marketing and persuasion. The dilution effect is that the audience averages the strength of a persuader’s arguments instead of adding the strengths. More arguments in favour of a position should intuitively increase the confidence in the correctness of this position, but empirically, adding weak arguments reduces people’s belief, which is why drug advertisements on US late-night TV list mild side effects in addition to serious ones. The target audience of these ads worries less about side effects when the ad mentions more slight problems with the drug, although additional side effects, whether weak or strong, should make the drug worse.

A persuader who believes her first argument to be strong enough to convince everyone does not waste valuable time to add other arguments. Listeners evaluate arguments partly by the confidence they believe the speaker has in these claims. This is rational Bayesian updating because a speaker’s conviction in the correctness of what she says is positively correlated with the actual validity of the claims.

A countervailing effect is that a speaker with many arguments has spent significant time studying the issue, so knows more precisely what the correct action is. If the listeners believe the bias of the persuader to be small or against the action that the arguments favour, then the audience should rationally believe a better-informed speaker more.

An effect in the same direction as dilution is that a speaker with many arguments in favour of a choice strongly prefers the listeners to choose it, i.e. is more biased. Then the listeners should respond less to the persuader’s effort. In the limit when the speaker’s only goal is always for the audience to comply, at any time cost of persuasion, then the listeners should ignore the speaker because a constant signal carries no information.

Modelling

Start with the standard model of signalling by information provision and then add countersignalling.

The listeners choose either to do what the persuader wants or not. The persuader receives a benefit B if the listeners comply, otherwise receives zero.

The persuader always presents her first argument, otherwise reveals that she has no arguments, which ends the game with the listeners not doing what the persuader wants. The persuader chooses whether to spend time at cost c>0, c<B to present her second argument, which may be strong or weak. The persuader knows the strength of the second argument but the listeners only have the common prior belief that the probability of a strong second argument is p0. If the second argument is strong, then the persuader is confident, otherwise not.

If the persuader does not present the second argument, then the listeners receive an exogenous private signal in {1,0} about the persuader’s confidence, e.g. via her subconscious body language. The probabilities of the signals are Pr(1|confident) =Pr(0|not) =q >1/2. If the persuader presents the second argument, then the listeners learn the confidence with certainty and can ignore any signals about it. Denote by p1 the updated probability that the audience puts on the second argument being strong.

If the speaker presents a strong second argument, then p1=1, if the speaker presents a weak argument, then p1=0, if the speaker presents no second argument, then after signal 1, the audience updates their belief to p1(1) =p0*q/(p0*q +(1-p0)*(1-q)) >p0 and after signal 0, to p1(0) =p0*(1-q)/(p0*(1-q) +(1-p0)*q) <p0.

The listeners prefer to comply (take action a=1) when the second argument of the persuader is strong, otherwise prefer not to do what the persuader wants (action a=0). At the prior belief p0, the listeners prefer not to comply. Therefore a persuader with a strong second argument chooses max{B*1-c, q*B*1 +(1-q)*B*0} and presents the argument iff (1-q)*B >c. A persuader with a weak argument chooses max{B*0-c, (1-q)*B*1 +q*B*0}, always not to present the argument. If a confident persuader chooses not to present the argument, then the listeners use the exogenous signal, otherwise use the choice of presentation to infer the type of the persuader.

One extension is that presenting the argument still leaves some doubt about its strength.

Another extension has many argument strength levels, so each type of persuader sometimes presents the second argument, sometimes not.

In this standard model, if the second argument is presented, then always by the confident type. As is intuitive, the second argument increases the belief of the listeners that the persuader is right. Adding countersignalling partly reverses the intuition – a very confident type of the persuader knows that the first argument already reveals her great confidence, so the listeners do what the very confident persuader wants. The very confident type never presents the second argument, so if the confident type chooses to present it, then the extra argument reduces the belief of the audience in the correctness of the persuader. However, compared to the least confident type who also never presents the second argument, the confident type’s second argument increases the belief of the listeners.

All public statues should be removed

There is no benefit to spending taxpayer money on creating or sustaining personality cults. The same goes for all public art – the current (local) government should not decide on which people to popularise. No significant market failure exists in physical art objects. The government thus does not need to intervene in the market for statues (copying digital art is another matter). Private individuals can put almost any statues and art on their own property as part of free speech.

The materials of which the statues are made could be used for something beneficial instead, like public housing for the poorest members of society. Clearly the government’s goal in erecting statues is to provide circus to the public in order to get re-elected, not to benefit society.

If the influential people whom the statues depict were asked whether the person or the idea matters more, my guess is that almost all would emphasise the idea. Most would ask the resources to be spent on more reasonable things than statues of them.

If the goal of a statue is to signal the importance of the ideas of the person depicted, then there are more efficient ways for this signalling. For example, a scholarship, a charity or a public library in the name of the person.

Food refused by the most people

Which food would the greatest fraction of the world population refuse to eat? To make the question interesting, focus on widespread food items, not „interesting” local specialties like surstromming, fermented shark, maggot cheese. My guess is that pork and beef would be the most widely refused, by Muslims and Hindus respectively. Meat in general is considered objectionable by more people than vegan dishes. Refusal of plant-based food is mostly due to allergies, so soy and wheat would be the least popular. In light of this, it is interesting that the main components of the British Airways snack box on 17 May 2020 were made of wheat and pork (Jamon Iberico and a spread made of 57% bacon and 18% pork jowl). The box replaced the usual airline meal. According to British Airways, the reason was to reduce food heating on the plane during the Covid-19 pandemic. I am not sure how reducing cooking is supposed to avoid infection, but even supposing that, the pork-based snacks do not seem optimal by any criterion.

Vegan food is generally cheaper, and among animal-source foods, chicken is the cheapest, followed by turkey. So price cannot be the reason for serving pork. Airlines may try to signal wealth or that they care about passengers by offering „premium” foods, e.g. meat, and not the cheapest kind. However, this signal is undermined by the plastic boxes for the meals, the sloppy mixture of foods in the main box and the small quantities. The goal is clearly not to feed people or to keep them healthy. It does not seem reasonable for the airline to expect that it will give passengers a good taste experience.

Popularity inequality and multiple equilibria

Suppose losing a friend is more costly for a person with few contacts than with many. Then a person with many friends has a lower cost of treating people badly, e.g. acting as if friends are dispensable and interchangeable. The lower cost means that unpleasant acts can signal popularity. Suppose that people value connections with popular others more than unpopular. This creates a benefit from costly, thus credible, signalling of popularity – such signals attract new acquaintances. Having a larger network in turn reduces the cost of signalling popularity by treating friends badly.

Suppose people on average value a popular friend more than the disutility from being treated badly by that person (so the bad treatment is not too bad, more of a minor annoyance). Then a feedback loop arises where bad treatment of others attracts more connections than it loses. The popular get even more popular, reducing their cost of signalling popularity, which allows attracting more connections. Those with few contacts do not want to imitate the stars of the network by also acting unpleasantly, because their expected cost is larger. For example, there is uncertainty about the disutility a friend gets from being treated badly or about how much the friend values the connection, so treating her or him badly destroys the friendship with positive probability. An unpopular person suffers a large cost from losing even one friend.

Under the assumptions above, a popular person can rely on the Law of Large Numbers to increase her or his popularity in expectation by treating others badly. A person with few friends does not want to take the risk of losing even them if they turn out to be sensitive to nastiness.

Multiple equilibria may exist in the whole society: one in which everyone has many contacts and is nasty to them and one in which people have few friends and act nice. Under the assumption that people value a popular friend more than the disutility from being treated badly, the equilibrium with many contacts and bad behaviour actually gives greater utility to everyone. This counterintuitive conclusion can be changed by assuming that popularity is relative, not a function of the absolute number of friends. Total relative popularity is constant in the population, in which case the bad treatment equilibrium is worse by the disutility of bad treatment.

In order for there to be something to signal, it cannot be common knowledge that everyone is equally popular. Signalling with reasonable beliefs requires unequal popularity. Inequality reduces welfare if people are risk averse (in this case over their popularity). Risk aversion further reduces average utility in the popular-and-nasty equilibrium compared to the pooling equilibrium where everyone has few friends and does not signal (acts nice).

In general, if one of the benefits of signalling is a reduction in the cost of signalling, then the amount of signalling and inequality increases. My paper “Dynamic noisy signaling” (2018) studies this in the context of education signalling in Section V.B “Human capital accumulation”.

Dark-coloured buildings and cars are silly

Many buildings in Australia, especially new developments, are black, dark grey or brown, or at least the roof is. Many cars are black (other dark colours are less prevalent). The dark colouring increases both cooling and heating costs, because it absorbs and emits solar and infrared radiation faster. In addition, the dark buildings are depressing and ugly. Dark-coloured cars are more difficult to notice, especially in low-visibility conditions, thus have more accidents. White or yellow vehicles are the safest (Lardelli-Claret et al. 2002, Solomon and King 1995).

For cars, the choice of black colour is probably caused by the owner’s desire to seem wealthy by making the car look expensive – limousines in films and popular culture are often black. For buildings, the association in people’s minds between colour and price is weak. If anything, light-coloured houses, reminiscent of Mediterranean villas and the White House, may slightly raise the owner’s status. The reason for dark-coloured roofs may be the cost – tar paper is a cheap material, easy to install. Windows may appear dark due to the one-way glass used. However, for walls, the cheapest material is usually bare concrete, as shown by its choice for purely functional structures (warehouses, barriers, piers, military buildings). For private dwellings, wood or brick may be the cheapest. Neither concrete, wood nor brick is particularly dark in colour, so the choice to build black or brown houses is puzzling. Maybe it is an architectural fad – fashions often trump practicality.

Feedback requests by no-reply emails

We value your feedback” sent from a no-reply email address shows not only that the feedback is not valued, but also that the organisation is lying. More generally, when someone’s words and deeds conflict, then this is informative about his or her lack of truthfulness. If in addition the deeds are unpleasant, then this is the worst of the four possibilities (good or bad deeds combined with honest admission or lying).

The fact of sending such no-reply feedback requests suggests that either the organisations doing it are stupid, needlessly angering customers with insincere solicitations, or believe that the customers are stupid, failing to draw the statistically correct (Bayesian) conclusion about the organisation.

Some organisations send an automated feedback request by email (Mintos) or post (Yale Student Health) in response to every inquiry or interaction, even ones that clearly did not resolve the problem. The information about the non-resolution could easily be scraped from the original customer emails, without wasting anyone’s time by asking them to fill out feedback forms. The inefficient time-wasting by sending feedback requests is again informative about the organisation.

Putting your money where your mouth is in policy debates

Climate change deniers should put their money where their mouth is by buying property in low-lying coastal areas or investing in drought-prone farmland. Symmetrically, those who believe the Earth is warming as a result of pollution should short sell climate-vulnerable assets. Then everyone eventually receives the financial consequences of their decisions and claimed beliefs. The sincere would be happy to bet on their beliefs, anticipating positive profit. Of course, the beliefs have to be somewhat dogmatic or the individuals in question risk-loving, otherwise the no-agreeing-to-disagree theorem would preclude speculative trade (opposite bets on a common event).

Governments tend to compensate people for widespread damage from natural disasters, because distributing aid is politically popular and there is strong lobbying for this free insurance. This insulates climate change deniers against the downside risk of buying flood- or wildfire-prone property. To prevent the cost of the damages from being passed to the taxpayers, the deniers should be required to buy insurance against disaster risk, or to sign contracts with (representatives of) the rest of society agreeing to transfer to others the amount of any government compensation they receive after flood, drought or wildfire. Similarly, those who short sell assets that lose value under a warming climate (or buy property that appreciates, like Arctic ports, under-ice mining and drilling rights) should not be compensated for the lost profit if the warming does not take place.

In general, forcing people to put their money where their mouth is would avoid wasting time on long useless debates (e.g. do high taxes reduce economic growth, does a high minimum wage raise unemployment, do tough punishments deter crime). Approximately rational people would doubt the sincerity of anyone who is not willing to bet on her or his beliefs, so one’s credibility would be tied to one’s skin in the game: a stake in the claim signals sincerity. Currently, it costs pundits almost nothing to make various claims in the media – past wrong statements are quickly forgotten, not impacting the reputation for accuracy much. 

The bets on beliefs need to be legally enforceable, so have to be made on objectively measurable events, such as the value of a publicly traded asset. By contrast, it is difficult to verify whether government funding for the arts benefits culture, or whether free public education is good for civil society, therefore bets on such claims would lead to legal battles. The lack of enforceability would reduce the penalty for making false statements, thus would not deter lying or shorten debates much.

An additional benefit from betting on (claimed) beliefs is to provide insurance to those harmed by the actions driven by these beliefs. For example, climate change deniers claim small harm from air pollution. Their purchases of property that will be damaged by a warming world allows climate change believers to short sell such assets. If the Earth then warms, then the deniers lose money and the believers gain at their expense. This at least partially compensates the believers for the damage caused by the actions of the deniers.

Golf as a cartel monitoring device for skilled services

Many explanations have been advanced for golf and similar costly, seemingly boring, low-effort group activities. One reason could be signalling one’s wealth and leisure by an expensive and time-consuming sport, another may be networking during a low-effort group activity that does not interfere with talking.

An additional explanation is monitoring others’ time use. A cartel agrees to restrict the quantity that its members provide, in order to raise price. In skilled services (doctors, lawyers, engineers, notaries, consultants) the quantity sold is work hours. Each member of a cartel has an incentive to secretly increase supply to obtain more profit. Monitoring is thus needed to sustain the cartel. One way to check that competitors are not selling more work hours is to observe their time use by being together. To reduce boredom, the time spent in mutual monitoring should be filled somehow, and the activity cannot be too strenuous, otherwise it could not be sustained for long enough to meaningfully decrease hours worked. Playing golf fulfills these requirements.

A prediction from this explanation for golf is that participation in time-consuming group activities would be greater in industries selling time-intensive products and services. By contrast, if supply is relatively insensitive to hours worked, for example in capital-intensive industries or standard software, then monitoring competitors’ time use is ineffective in restricting their output and sustaining a cartel. Other ways of checking quantity must then be found, such as price-matching guarantees, which incentivise customers to report a reduced price of a competitor.

Star job candidates benefit from appearing to be worse

Employers have a cost of making a job offer: filling out forms, getting approval, not being able to make other offers simultaneously in case too many job candidates accept, etc. A company who believes that it is not the top choice of candidates would want to avoid making an offer to a star applicant (one who is likely to receive better alternative offers from top employers, thus turn down the lower-ranked company’s offer).

If the star job-seeker is uncertain about the offers she or he will get, or wants a bargaining chip to use with the most preferred company, then (s)he prefers to obtain the lower-ranked employer’s offer, even when planning to reject it. A way to entice the company into offering a job is to pretend to be more attainable (have a worse outside option) by faking lower talent and potential when interviewing with lower-ranked employers. For this pretence to be (partly) credible, it must have a cost for the job-seeker, otherwise all the best candidates would pretend to be worse and increase their chance of obtaining offers from their backup employers. Then the next-best candidates would have to fake being less good to receive jobs, etc. This race to the bottom would only end once all candidates look like the worst possible, which does not seem realistic.

One potential cost is that faking lower talent has a random outcome, which may be so bad that the employer does not want to offer a job at all. This would temper the incentive to appear worse. Another cost is information leakage – if bad performance at a less desirable interview becomes known to higher-ranked employers, then the candidate may forfeit her or his most preferred interviews and jobs. It could also be that the top job-seekers cannot hide their quality, for example because their genius shines out despite their best effort, or employers base offers solely on recommendation letters, which the candidate cannot see or affect around the time of applying.

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.