Utilitarian Statistics

Mark Pottenger


I am writing this in June 2021, so most numbers below are from May or June of 2021.

Fair ethics

Human brains are wired to appreciate fairness, but there is, as in almost all things, room for considerable individual variations. These are just a few of the links that came up in a quick search for brain fairness: How Fairness Is Wired in the Brain, Fairness is in the brain, scientists say, and Decoding fairness motivations from multivariate brain activity patterns.

Divide and choose (or cut and choose) is a protocol for two people to fairly divide resources (like cutting a cake). One person cuts the cake, and the other person chooses which piece they will take. This generally satisfies both people that the resource (e.g., cake) was divided fairly.

The Golden Rule, to treat others as you would like others to treat you, is present in a variety of formulations in many religions and cultures.

Utilitarianism is an ethical theory based on the idea of maximizing happiness and well-being. My memory from years ago was the phrase "the greatest good for the greatest number", but when I recently looked up Utilitarianism in Wikipedia, the initial discussion was more about happiness than good. Utility, in this concept, is anything that augments individual happiness. The complete theory includes a lot of complications beyond the root principle: you need to look at strengths of effect, numbers of people affected both positively and negatively by any action, first and second order consequences, and more. Treating the interests of all people equally is central.

"Commons" is a term from economics for resources (natural resources such as air or water, and cultural resources such as literature or music) available to all members of a society (not privately owned). "Public good" is a related term. The "free-rider problem" is something that happens when users of resources or public goods don't pay enough for their use. This can degrade the resources or provoke negative reactions from users who are paying for the resources.

Decisions and actions

Taking fairness or the Golden Rule or Utilitarianism as our ethical framework, what sort of responses to the COVID-19 pandemic and some other contemporary issues should we want?

First, our actions should be guided by facts, not fantasies, fallacies, or falsehoods.

We can't recommend actions to produce the greatest good if we don't know the true state of the world our actions will occur in.

So our first action needs to be to learn how to tell fact from fiction, to learn what sources of information are parts of reality networks and what sources are disinformation from networks of liars.

A corollary is a point in my brief essay about Responsible Speech: don't pass on the disinformation of the liars.

The pandemic

Our knowledge about COVID-19 has gone from zero to quite a bit in a year and a half, even though there is still a huge amount to learn. That knowledge lets us say with certainty that vaccinations are in the best interests of everybody in the world. Catching the disease has a MUCH higher risk of death, and surviving the disease has a much higher risk of disabilities or the many dangers of "long COVID", than all possible side effects of any of the available vaccines.

From a WHO site: Globally, as of 4:55pm CEST, 7 June 2021, there have been 173,005,553 confirmed cases of COVID-19, including 3,727,605 deaths, reported to WHO.

That works out to about 2% of confirmed cases dying, but we don't know the actual rate because of HUGE data uncertainties cause by under-reporting, misreporting, failures to test, test errors, and more. The U. S. rate works out to slightly under 2%, with as much or more uncertainty because of the way COVID-19 response was politicized and bungled.

Much of the impact of the COVID-19 pandemic has been due to many flaws in world-wide healthcare. Despite years of scientific warnings that new diseases are inevitable, the healthcare systems of most countries were not ready with stockpiles of personal protective equipment (PPE), public health regulations, contact tracing systems, hospital capacity, etc. The many actions taken were uncoordinated and often only partly effective, leading to waves of infection that overwhelmed hospital capacity and healthcare workers. This is still going on in many parts of the world.

Public health measures

Lockdowns are extreme measures that protect health by keeping people away from all other people.

Distance between people and good ventilation reduce risk by reducing the amount of virus getting from infected people to vulnerable people.

There are cloth, surgical, and N95 masks for infection control, and their effectiveness varies with fit and number of layers. I found these numbers, though they cover a mix of mask types:

Mask wearing by the infected reduces risk of spreading COVID-19 by 50% to 80%.

Mask wearing by the vulnerable reduces risk of catching COVID-19 by 70% to 79% in an infectious environment.


The only long-term solution to a pandemic is vaccination. Vaccination reduces the odds of catching a disease, then spreading it, and makes symptoms less severe if you do catch it. Taking no public health actions results in unacceptable numbers of deaths. All non-vaccine public health actions only slow or lessen disease impact, leading to the high death rates we have all seen. The first vaccines against the SARS-CoV-2 virus that causes COVID-19 were available less than a year after development started only because they used technology that is the end of a chain of decades of scientific discoveries and technological developments.

About 45% of people in California are fully vaccinated.

About 42% of people in the U. S. are fully vaccinated.

World-Wide, only about 6% of people are fully vaccinated.

For the pandemic to be over, we need to reach herd immunity levels of vaccination (70% or 80% or 90% or more) world-wide, so we clearly have a LONG way to go.

The vaccine side effects I could find listed at the CDC are:

Anaphylaxis (severe allergic reaction): 2 to 5 people per million vaccinated.

Thrombosis with thrombocytopenia syndrome (TTS) after J&J/Janssen COVID-19 vaccination: 32 cases after 10.2 million vaccinated (3 per million).

Myocarditis and pericarditis in adolescents and young adults: monitoring, no rates yet.

Deaths: monitoring is ongoing—no causal links have been identified yet except TTS after the J&J vaccine (above). The CDC site reports a count of deaths of vaccinated people, but without a lot more actuarial information there is no way to know if that count is less or more than usually expected for that population.

Vaccine effectiveness:

The two-dose mRNA (Pfizer-BioNTech and Moderna) vaccines reduce COVID-19 risks by 90% or more. For people who catch the disease despite vaccination, they make symptoms less severe & provide protection against severe illness.

Since the mRNA vaccines don't include any actual COVID-19 viruses, it is actually completely impossible to get COVID-19 from these vaccinations, placing all claims of that happening firmly in the falsehoods file.

A breakthrough infection rate measures how many people catch a disease after they are vaccinated against it. The latest numbers I've seen for COVID-19 breakthrough infection rates are 0.04% and 0.03% for two counties in California (3 or 4 people per 10,000), with very few deaths among those cases. Another source said that of 135 million U. S. people fully vaccinated by June 1, 0.002% (2 per 100,000) of fully vaccinated people were later hospitalized for COVID-19, and only 0.0004% (4 per million) died.

The level of vaccination in the U. S. has already reduced the spread of the disease enough for many health experts to approve reductions in shutdowns, distancing, and mask-wearing requirements for FULLY VACCINATED PEOPLE, but until a much larger percentage of the population of the whole world is vaccinated, many restrictions and precautions remain necessary.

The level of vaccination we have reached still leaves the disease spreading patchily in the U. S. and widely in many other countries, leading to outbreaks and surges and high risks of new variants of the virus evolving that may circumvent the immunity conferred by the current vaccines.

Even in the U. S., we have not yet reached the ideal goal of vaccination campaigns for any disease: herd immunity. This is when a high enough portion of the population has immunity to STOP the disease from spreading. Herd immunity also protects people who CAN'T get vaccinated because they are too young or have compromised immune systems or preexisting health conditions that make any vaccination unsafe for them. Without much stretching, herd immunity can be viewed as a commons or public good, subject to the free-rider problem. People who could but don't get vaccinated benefit from the efforts of the people who do get vaccinated. However, the biggest danger coming from widespread anti-vaccine disinformation spread by both sincere and opportunistic anti-vaxxers is the possibility that not enough of the population will get vaccinated to reach herd immunity, requiring years more of public health safety measures (shutdowns, distancing, mask-wearing, etc.) and creating high risks of new variants of the virus. The longer the virus is active (not stopped by herd immunity) and the more people it infects, the more opportunities it has to mutate, increasing the danger of more infectious and/or more deadly strains/versions/variants evolving.

With what we know so far, practicing Golden Rule ethics should lead everyone old enough to be eligible for COVID-19 vaccination, and healthy enough for any vaccination, to get vaccinated as soon as possible.


How likely is anyone to catch COVID-19 in a given situation?

The starting point is how widely the virus is circulating in the population in the area, a number that is currently going down in areas with good vaccination rates, but which has surged multiple times elsewhere.

Staying outside or in well-ventilated indoor locations reduces risk, though I didn't find percentages.

Everyone properly wearing good masks reduces risk. Using the 70% reduction value from the range of values I found, the risk when both infected and vulnerable people are masked is 30% x 30%, or 9% of the risk when nobody is masked. This is an example of principles, not a final number—I picked one value from a range and the actual masks used and how well people use them will change the percentages.

Being fully vaccinated greatly reduces risk. Just vaccination reduces the risk to breakthrough infection rates of 0.04% or 0.03% (3 or 4 people per 10,000 vaccinated). Beyond reducing the risk of infection, vaccination also reduces the severity of the disease when there are breakthrough infections, with about 5% of infections (0.002% of the vaccinated population, or 2 per 100,000) needing hospitalization and about 20% of the 5% hospitalized dying (0.0004% of the vaccinated population, or 4 per million). [The percentages I used in the middle are iffy because they are converting numbers from California to numbers from the whole U. S.]

Add consistent use of masks to vaccination and you reduce your breakthrough infection risk to 30% x 0.04%, or 0.012% (1.2 per 10,000). Add consistent use of masks by anyone nearby who is infected, and your risk goes down to 0.012% x 30%, or 0.0036% (3.6 per 100,000). [This whole calculation is iffy because I have no way of knowing how much mask use there was while the breakthrough infection numbers were collected, given the chaotic mix of responses to the pandemic.]

More Brains

While searching for fairness in the brain, I saw reminders of the term Theory of Mind (ToM). This is the ability of a person to imagine mental states of others and to empathize. Like all human characteristics, this varies in strength. People with weaker brain support for ToM are less able to empathize. I've seen a lot more of that in recent news than bodes well for all of us.

More Fairness

The cries for social justice that have accelerated in the last year are another manifestation of many people's deeply rooted desire for fairness. U. S. cultures and laws have deeply entrenched racism and sexism and other biases preventing fair/equal treatment of many people.

As one article put it, equity (being fair and impartial) is a practice that helps achieve the goal of equality (being equal).

Equal employment opportunity in the U. S. is supposed to be protected since the Civil Rights Act of 1964, but plenty of discrimination and inequity still exists. Both laws and cultural values are still very much works in progress.

Current U. S. tax structures are a long way from fairness—they are heavily rigged to favor the rich in ways that have been increasingly concentrating wealth in a small minority for decades. Income inequality is a real problem causing real damage to society and to the economy. The problems will only get worse until the laws get fixed.

Since selfishness and desire for fairness are human characteristics that vary widely, we can't naively count on the goodness of people in general to produce a fair/just/equitable society. Many laws and regulations already exist to impose fairness that some people and companies (run by people) would otherwise avoid, but many other laws support unfairness (like the U. S. tax system) and need to be repealed or amended, and many more laws and regulations to impose fairness are still needed.

Political notes

Good political labels are a bit hard to find in the modern U. S. The right and left labels go back to the seating of a legislative body a couple centuries ago. The blue and red labels go back to the color scheme of some TV election maps decades ago. The conservative label is grossly misused, because the people claiming it are trying to make radical changes to U. S. culture, not trying to conserve or preserve it. Most so-called conservatives in the U. S. these days seem to be focused on seeking preference and advantage for their narrow tribal in-groups, constantly violating Golden Rule ethics (and often qualifying as free riders in commons). They have also become so wedded to lies that it makes decisions based on facts almost impossible. The liberal label is the only one that seems to be used moderately correctly, since the label is usually applied to people who favor liberty and equality.

There is far too much talk in U. S. politics and culture in general about rights, and far too little talk about responsibilities.

Copyright © 2021 Mark Pottenger

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