# Calorie claims of exercise classes and Strava

This machine burns more calories per minute than any other– up to 800 calories in a 45-minute session” (SWEAT by BXR | VersaClimbing)

Strava shows: Morning Elliptical 1h36m 1,115Cal 136bpm.

If the ad and Strava mean calories (small calories), not kilocalories (large calories), then the unit Cal must be a typo for cal – s

Both “up to 800 calories in a 45-minuteand 1,115 cal in 1h36m are less than the basal metabolic rate of 1200kcal/day =50kcal/h =50,000cal/h. The marketing claims probably intend to say kilocalories.

The sustained (an hour or more) power output of elite cyclists is about 400W. ()

1W =1J/s =3600J/h, so 400W =1440kJ/h =344 kcal/h because a calorie is 4.184 Joules.

Less-than-elite athletes likely burn significantly fewer calories than 344kcal in an hour, especially when not competing. Any exercise class, app or sports watch claiming over 200 kcal/h is suspect.

# Dilution effect explained by signalling

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

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.

# Clock and ads projected on the ceiling

At a public swimming pool, the clocks on the wall are usually small, far and hard to see through droplet-covered goggles. The clock is relevant for planning to finish by a certain time and for tracking one’s speed (lap time). A solution is to use a projector to show a large clock on the ceiling, or to draw the numbers on the ceiling with a laser – essentially a programmed pointer.

The ceiling is also an untapped advertising display space, not just at swimming pools and gyms, but in any building. Ceiling ads are more valuable in swimming pools, gyms and yoga studios than in most other structures, because people doing backstroke, bench press or fish pose are facing the ceiling, which is not the case in a majority of buildings.

The floor is also mostly unused ad space. Projecting ads on the floor is not as useful as the ceiling, because people walking through the projector beam block the display.

# Prefereeing increases the inequality of research output

Why do top researchers in economics publish almost exclusively in the top 5 journals? Random idea generation and mistakes in the course of its implementation should imply significant variance of the quality of finished research projects even for the best scientists. So top people should have more of all quality levels of papers.

Nepotism is not necessary to explain why those at top universities find it easier to publish in top journals. Researchers at the best departments have frequent access to editors and referees of top journals (their colleagues), so can select ideas that the editors and referees like and further tailor the project to the tastes of these gatekeepers during writing. Researchers without such access to editors and referees choose their projects “blindly” and develop the ideas in directions that only match gatekeeper tastes by chance. This results in much “wasted work” if the goal is to publish well (which may or may not be correlated with the social welfare from the research).

In addition to selecting and tailoring projects, those with access can also better select journals, because they know the preferences of the editorial board. So for any given project, networking with the gatekeepers allows choosing a journal where editors are likely to like this project. This reduces the number of rejections before eventual acceptance, allowing accumulating publications quicker and saving the labour of some rounds of revision of the paper (at journals that reject after a revise-and-resubmit for example).

A similar rich-get-richer positive feedback operates in business, especially for firms that sell to other firms (B2B). Top businesspeople get access to decisionmakers at other organisations, so can learn what the market desires, thus can select and tailor products to the wants of potential customers. Better selection and targeting avoids wasting product development costs. The products may or may not increase social welfare.

Information about other business leaders’ preferences also helps target the marketing of any given product to those predisposed to like the product. Thus successful businesspeople (who have access to influential decisionmakers) have a more popular selection of products with lower development and marketing costs.

One friction is an agency conflict between managers and shareholders. If managers are evaluated based on relative performance, then the managers of some firms may collude to only share useful information with each other, not with those outside their circle. The firms managed by the circle would benefit from wider sharing of their product needs, because outside companies would enter the competition to supply them, reducing their costs. However, those outside firms would get extra profit, making their managers look good, thus lowering the relative standing of the managers in the circle.

# „People should have a choice” works both ways

Initiatives to counter unhealthy and destructive habits (smoking, gambling, junk food consumption) by taxing or restricting the addictive goods and services are often opposed with the argument that people should have a choice. One counterargument is that removing temptations from one’s future self is also a choice that people should have. For example, banning oneself from casinos. Similar registries could be instituted to ban oneself from buying alcohol or tobacco – the sales already require checking ID, so all that is needed is to compare the person’s identity against a database. For example, using a machine-readable ID which causes the machine to display “Do not sell” for people who have put themselves on the relevant list. Countries with universal machine-readable identification documents can use their existing systems for this. Examples are the European Union national identity cards.

Other ways to remove temptations from one’s way are restrictions on advertising, eliminating vending machines from a building, liquor stores near schools, alcohol and tobacco from the more visible areas of grocery shops. Just like people should have a choice to block spam emails, calls, web browser ads, they should have a choice to ban street advertising (of addictive goods or anything else) in their residential or work areas. Removing a public ad restricts some people’s right to see it, but empirically most people do not want to see more marketing in public spaces or elsewhere. Symmetrically, displaying a public ad restricts people’s right to avoid seeing it, so the question is how many people’s rights are restricted by banning vs allowing advertising.

The problem of annoying public advertisements may be resolved by smart glasses like Google Glass if these can detect advertisements appearing in the field of view and block these or replace with other images before the user sees these, similarly to how adblock software in browsers works.

# 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.

# Blind testing of clothes

Inspired by blind taste testing, manufacturers’ claims about clothes could be tested by subjects blinded to what they are wearing. The test would work as follows. People put clothes on by feel with their eyes closed or in a pitch dark room and wear other clothes on top of the item to be tested. Thus the subjects cannot see what they are wearing. They then rate the comfort, warmth, weight, softness and other physical aspects of the garment. This would help consumers select the most practical clothing and keep advertising somewhat more honest than heretofore. For example, many socks are advertised as warm, but based on my experience, many of them do not live up to the hype. I would be willing to pay a small amount for data about past wearers’ experience. Online reviews are notoriously emotional and biased.

Some aspects of clothes can also be measured objectively – warmth is one of these, measured by heat flow through the garment per unit of area. Such data is unfortunately rarely reported. The physical measurements to conduct on clothes require some thought, to make these correspond to the wearing experience. For example, if clothes are thicker in some parts, then their insulation should be measured in multiple places. Some parts of the garment may usually be worn with more layers under or over it than others, which may affect the required warmth of different areas of the clothing item differently. Sweat may change the insulation properties dramatically, e.g. for cotton. Windproofness matters for whether windchill can be felt. All this needs taking into account when converting physical measurements to how the clothes feel.

# M-diagram of politics

Suppose a politician claims that X is best for society. Quiz:

1. Should we infer that X is best for society?

2. Should we infer that the politician believes that X is best for society?

3. Should we infer that X is best for the politician?

4. Should we infer that X is best for the politician among policies that can be `sold’ as best for society?

5. Should we infer that the politician believes that X is best for the politician?

This quiz illustrates the general principle in game theory that players best-respond to their perceptions, not reality. Sometimes the perceptions may coincide with reality. Equilibrium concepts like Nash equilibrium assume that on average, players have correct beliefs.

The following diagram illustrates the reasoning of the politician claiming X is best for society: M-diagram of politics In case the diagram does not load, here is its description: the top row has `Official goal’ and `Real goal’, the bottom row has `Best way to the official goal’, `Best way to the real goal that looks like a reasonable way to the official goal’ and `Best way to the real goal’. Arrows point in an M-shaped pattern from the bottom row items to the top items. The arrow from `Best way to the real goal that looks like a reasonable way to the official goal’ to `Official goal’ is the constraint on the claims of the politician.

The correct answer to the quiz is 5.

This post is loosely translated from the original Estonian one https://www.sanderheinsalu.com/ajaveeb/?p=140

# Claims that tickets are running out

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.

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.

# Free wifi lies

Many airports, hotels and other public places advertise free wifi, but in a significant fraction of them, the wifi does not work, e.g. in Doha Airport. One view about this is that you get what you pay for. On the other hand, the claim of providing free wifi makes people try to connect and wastes their time. Everyone would be slightly better off if the non-working wifi was not advertised – the advertiser would save the cost of printing the „Free wifi” signs and the visitors would save time.

It is cheap for the service provider to check whether the wifi is in fact working – just program a few cheap used smartphones to periodically try to connect to the wifi and send a notification to IT if the connection attempt fails. The connection failure may even trigger an automatic restart of the router.

Some airports may have wifi available, but only to a restricted group of people. For example, in India, connecting requires a local phone number, which most international travellers do not have. In Singapore and Shanghai airports, the wifi requires either a local number or scanning one’s passport in a kiosk, and the kiosks are sometimes out of order. Again, looking for the kiosk and trying to scan wastes time.

Intermittent wifi may be better or worse than none, depending on what fraction of time it is available and people’s average time cost of trying to connect.