The Houses of Parliament at the end of an empty Westminster Bridge in central London on March 24, 2020, after Britain ordered a lockdown to slow the spread of Covid-19. Photo: AFP/Justin Talis

In war, the commander must choose who is to live and who is to die. On the offensive, he sends in a diversionary force to be annihilated by the enemy, so as to draw enemy forces away from the main point of attack. On the defensive, he chooses which divisions will be left to the enemy to destroy. His decisions are made in an effort to maximize the likelihood of victory.

Perhaps the cost of victory is too high. The optimal decision leaves too many dead, even if it achieves the objective of victory. The cost of the dead must be taken into account. Winston Churchill faced this decision after the fall of France in World War II. Many urged coming to terms with the Germans, which would have meant political domination by Germany. Churchill chose war. He won the gamble and is considered among the greatest leaders in history.

A salient problem in statistics and engineering is to choose an optimal decision from among a collection of possible decisions. The basic ingredient is a cost function that needs to be minimized by the decision. Where there is a single cost to minimize, decisions are not so difficult; however, when there are multiple competing costs making up the overall cost, these must be assigned weights to reflect their importance, and then matters are more complicated. Different people may assign different weights.

Decisions are made with uncertain knowledge of the present and uncertain predictions of the future. The cost must be evaluated relative to the uncertainty. Different people may assess and incorporate uncertainty in different ways. A basic approach to uncertainty is to take an action that minimizes the expected cost based on some statistical assumptions. Naturally, a decision based on expected outcomes may lead to consequences that were thought to be unlikely. Another approach is to take a “minimax” action that minimizes the maximum cost (choose the action with the best worst-case outcome). No matter how one proceeds, everything is relative to the cost function.

In a much-discussed article in STAT, Professor John Ioannidis, the C F Rehnborg Chair in Disease Prevention at Stanford University, is critical of bandying about alarming, meaningless statistics related to the novel coronavirus that causes Covid-19. These have been computed from small, unrepresentative, non-random samples. The data do not exist to give even marginal credence to predictive scientific models. Ioannidis raises many questions with regard to lack of data.

He writes:

“The most valuable piece of information for answering those questions would be to know the current prevalence of the infection in a random sample of a population and to repeat this exercise at regular time intervals to estimate the incidence of new infections. Sadly, that’s information we don’t have. In the absence of data, prepare-for-the-worst reasoning leads to extreme measures of social distancing and lockdowns….

“We don’t know how long social distancing measures and lockdowns can be maintained without major consequences to the economy, society, and mental health. Unpredictable evolutions may ensue, including financial crisis, unrest, civil strife, war, and a meltdown of the social fabric.”

In sum, first, we lack the data to construct statistical models that would allow us to use any other criteria than minimax (worst-case), and, second, a proper cost function should involve numerous objectives that are not being accounted for.

In a follow-up article in STAT, Professor Marc Lipsitch, director of Harvard’s Center for Communicable Disease Dynamics, agrees with Ioannidis on the lack of data, but argues:

“Ioannidis is right that the prospect of intense social distancing for months or years is one that can hardly be imagined, let alone enacted. The alternative of letting the infection spread uncontrolled is equally unimaginable. We certainly need more data. Even more than that, we need a breakthrough to make effective treatments, vaccines, or other preventive measures available at scale.

“Waiting and hoping for a miracle as health systems are overrun by Covid-19 is not an option. For the short term there is no choice but to use the time we are buying with social distancing to mobilize a massive political, economic, and societal effort to find new ways to cope with this virus.”

Professor Lipsitch’s argument is strong, so long as we accept his cost function: death and suffering in the near future, and the overrunning of health-care systems. But where are “financial crisis, unrest, civil strife, war, and a meltdown of the social fabric?” If economic models (also unreliable) predict depression, inflation, destitution of the working class, and long-term depreciation of health care owing to economic decline, then Lipsitch’s argument is weaker, even though the recognition of today’s suffering is not diminished an iota. Of course, a broader cost function might lead to precisely the action proposed by Professor Lipsitch.

The US, and the world, face decisions that must be made in the context of enormous uncertainty and lack of data. US President Donald Trump’s decisions will increase the risk to certain people as opposed to others, and this must be done relative to the cost assessment made by his team. Neither he nor his presidential predecessors are economists, epidemiologists, or scientists. He is confronted with an optimization of great statistical difficulty, almost surely not fully understood by the medical experts around him.

There are outstanding statisticians in the federal research labs and universities. One can only hope that some are having serious input. But in the end, the decision will hurt some, and its effects may take years to judge.

Regarding the effects, Professor Ioannidis’ concern for the social fabric is not overblown. In whatever manner the costs are weighed and decisions made, one should keep in mind what every good Marxist knows: Liberty is a luxury of people with full stomachs. How full depends on the bonds that hold a people together.

In his first Inaugural Address in 1933, in the midst of the Depression, US president Franklin Roosevelt stated:

“We face the arduous days that lie before us in the warm courage of the national unity; with the clear consciousness of seeking old and precious moral values; with the clean satisfaction that comes from the stern performance of duty by old and young alike. We aim at the assurance of a rounded and permanent national life.”

Years later, when Roosevelt met with Winston Churchill on HMS Prince of Wales in August 1941, four months prior to the bombing of Pearl Harbor, they and the crews participated in a joint religious service, during which they sang “Onward Christian Soldiers.” Of the moment, Churchill said, “The same language, the same hymns, and more or less the same ideals.… It was a great hour to live.” This, while German U-boats were pummeling British shipping and the German army was moving, seemingly unstoppable, toward Moscow.

Roosevelt had called upon “national unity” and “precious moral values” to confront the economic devastation of the Depression. Churchill called upon the ancestral, political, and religious bonds between the two nations. These bonds were part of Roosevelt’s cost function: The defeat of Britain was a cost that he was not willing to accept.

How strong are the bonds that hold the social fabric together today?

Edward R Dougherty

Edward Dougherty is distinguished professor of engineering at Texas A&M University.