The Risk of Not Being Vaccinated

Who will be left out of the herd when a vaccination program comes to its end?

Posted Dec 16, 2020

 Joseph Mazur
Vaccinating chance
Source: Joseph Mazur

Successful anti-vaccine disinformation will muddy the already sullied intelligence of risk in not getting vaccinated, so what are the odds of surviving COVID without a vaccination?

At the turn of the 19th century, the typical gambler in America knew almost nothing of the mathematics of risk but did have a sense of the rarity of poker hands—that drawing a full house is almost a hundred times more likely to happen than drawing a straight flush, and that a straight is almost twice as likely as a flush. Such information was part of the culture, though it wouldn’t have taken much mathematics to figure it out.

We are now living with a virus that has killed more than 304,000 people in the U.S. More than 17 million Americans have tested positive. Testing positive means your health situation could be OK or somewhere between “not good” and death; moreover, it means that you have a non-zero probability of long-term consequences or death. And still, so many Americans believe that because many COVID patients beat the virus, they can too.

In this early 21st century, Americans have almost no sense of the mathematics of risk, even though their lives now depend on it.

Risks are the gambles, the games, the balance of expectation and fate. And luck rarely comes without risking the possibility of loss, injury, trouble, vulnerability, ruin, or damage in a universe of opposing chances.

Soon, many of us will have the option of getting a COVID vaccine with a 95 percent chance of keeping us safe. But who are the “us” that will be safe? The latest Gallup Poll estimates that 42 percent of Americans have decided not to get the vaccine. Many of those people mistakenly believe that there is a strong chance that an illness far worse than that of the virus will follow vaccine inoculations.

It’s just a poll, of course, but well-designed polls do translate into rough numbers. In this case, almost 140 million Americans! That does worry me. Not for myself, but rather for those who are misunderstanding the odds of not accepting a gift to stay alive long enough to get to their natural end date. So why are so many Americans willing to gamble with their lives in following crushingly debunked COVID conspiracy theories fabricated by trendy manifestos?  

I suppose it is the belief of good fortune, a belief encouraged and reinforced by earlier gratifying escapes from failure and rewards of success. The gambler dealt a straight flush believes it will soon happen again.

We could view the decision of not accepting the gift of a vaccine as a poker game based on a risk-reward evaluation. With poker, you may compute the probabilities of being dealt a favorable card. You have to weigh the risk of not getting a fortunate card against how badly it would be to lose the pot. You have to assess the odds of your hand overriding the one you are trying to beat.

The same is true with a vaccine decision, where “losing the pot” translates to death or a near-death experience. The amount of risk you are willing to take should be less than the return you are likely to clear.

The stake is life.

Much of gambling behavior rests on immediately prior gains or losses. For many, winning a hundred dollars at a slot machine is a strong incentive for risking those same hundred dollars on a game with wildly skewed odds. There is a feeling that you are playing with the house’s money and that it’s free money to lose.

Gambling choices are rarely made by accounting for past losses; they come from the witnessing of former fortune outcomes. So what we find is that people feel that the longer they survive being COVID-free, the more hope they have to live through the crisis safely.

It may be the reason why some Americans continue to mingle with others, maskless. They have survived COVID so far. That survival is equivalent to being given house money, extra time to live with or without a mask, a gift that brings with it the illusion of being invincible.

When it comes to human behavior and the management of risk, we find apparent contradictions. Behavior toward risk depends not only on how that risk is considered but also on risk-taker views of gains and losses: that is, whether one is a risk-averting or risk-seeking person.  

Conspiracy theories travel from someone believable to someone gullible.

Within behavioral psychology, there is personality theory, which presumes that an individual behaves per his or her personality type. In this camp, the question remains whether or not a dominant personality is genetically determined or dependent on life’s experiences. For example, some psychoanalysts pointed to early childhood problems with parental approval and the unconscious perception of denied love, so the gambler turns to luck for love and acceptance. Personality theory attributes decisions to environmental influence, with consciously learned, habitual responses to external stimuli that may appear at any stage of life.

What holds for personalities applies to communities. The view of a neighborhood is something that evolves by migration. For one hundred years, from 1860 to 1960, Vermont, the state I live in, voted Republican in every presidential election. Look at it now. For the last 24 years, it has never voted for a Republican president.

Fortunately, at any stage of life, it is possible to unlearn anything learned. Some behavioral psychologists believe that rewards reinforce repetitive behavior. For the decision to accept a COVID vaccine, the payment is the safety of immediate health. For the decision to turn down a COVID vaccine, an incentive is avoiding any complications that might arise from a hidden but dangerous side effect. Some considerations may come from social media conspiracy theories.

Immediate surroundings often reinforce behavior and its consequences, and that reinforcement gets regularly repeated. A friend relays something you had already seen many times on Facebook and Twitter that falsely claims all COVID vaccines make people sterile.

The Center for Countering Digital Hate (CCDH) reports that 31 million people follow anti-vaccine groups on Facebook, and 17 million people follow those same groups on YouTube. It warns: “The decision to continue hosting known misinformation content and actors left online anti-vaxxers ready to pounce on the opportunity presented by coronavirus.”

No one should underestimate the risk.

With the end of the pandemic near, Sarah Zhang, in the Atlantic, calls the next six months “vaccine purgatory.” It will be a period of suspicion of efficacy and side effects, bringing delays in getting back to a life that we once thought of as normal.

We are competing with Russian disinformation, as exemplified in statements like this one posted on Facebook and Twitter accounts coming from Kirill Dmitriev, chief executive of the Russian firm financing Sputnik V, the Kremlin’s vaccine. 

Western vaccine manufacturers rely on experimental, little studied, and not proven in the long-term technologies, encountering obstacles in their clinical trials.

Purgatory, it will be if 140 million Americans fear complications of side effects attributed to any of the emerging vaccines. Many, beyond the 140 million, are concerned about the rushed testing. 

I’m not a psychologist. I am, however, a mathematician who has written extensively about odds and gambling. So take what you like from what I say. I can foresee what might happen when the bombardment of COVID vaccine disinformation builds a science-doubting fringe alliance from a growing number of credulous people who know nothing about the mathematics of risk.

We need more than just a majority of Americans vaccinated to protect themselves, their neighbors, and loved ones.

If, when given a chance, 140 million Americans decide not to be vaccinated, we shall still get to herd immunity, but the consequential herd will include only those who have immunity, and we do not know how long those immunities will last. One does not have to know anything about the mathematics of risk to understand that those who remain among the 140 million not vaccinated will be outside the herd, hoping to draw a flush to survive over a straight flush with death. It’s not easy to calculate the mathematical odds, but seriously, no one needs to do the calculation to know what is risk-wise and proper to do.

© 2020 Joseph Mazur


Joseph Mazur, What’s Luck Got to Do with It? The History, Mathematics, and Psychology Behind the Gambler’s Illusion (Princeton, New Jersey: Princeton University Press, 2010), 42.

“On Gambling,” American Imago, Vol. 4. (1947) pp. 61-77  and J. Gladston, “The Gambler and His Love,”  American Journal of Psychiatry, Vol. 117, (1960) pp. 553-555. Vol 2 October 2020