Justin McBrayer

# Vaccines, Unknown Risks, and Expected Value

News last month that the FDA has granted full approval to the Pfizer vaccine for COVID should relieve the vaccine hesitancy of some Americans. But by itself, this news won’t be a panacea.

[This article is an expanded version of an op-ed that ran Tuesday, September 21 in the * Albuquerque Journal*.]

Most of my friends and family who have not yet gotten the COVID vaccine are concerned about the long-term, unknown consequences from the inoculation, and the FDA approval doesn’t rule that out. After all, the FDA's decision is based on what they know at present, and the vaccines haven't been around very long. If there's some terrible side-effect yet to come, the FDA isn't likely to know about it yet.

My friends and family aren’t the only ones concerned about potential negative side-effects of the vaccine. A new YouGov survey shows that 90% of Americans who have opted against the vaccine are concerned about future side effects, and a recent article in Vox sums it up this way: “A significant portion of Americans don’t believe the vaccines are worth the potential downsides.” The standard reasoning goes like this: (a) most COVID infections aren’t bad, (b) we can’t rule out terrible vaccine side-effects in the future, and (c) the vaccine doesn’t fully protect you, anyway. So why risk it? Conclusion: don’t get the vaccine.

This reasoning is bad. And it’s bad because it selectively factors in only some of the unknown risks. Once **all** of the unknown risks are properly accounted for, getting a vaccine is the only rational option for most people.

Here’s why. Rational action maximizes expected value. If you want a cold beer and go to the refrigerator, you acted rationally. If you want a beer and go to the pantry, you didn’t. Given what you know about the probabilities of finding cold beer and given your priorities, going to the fridge is the rational strategy—it’s the one most likely to pay off. The same strategy applies to decisions about careers, vacations, and so forth.

In a similar way, the rational strategy to deal with COVID will be the one that is most likely to pay off. And here’s where unknown risks come into play: some people think that the winning strategy is to skip the jab because we are in the dark about the potential for long-term, negative side effects of the vaccine. It's not that these folks think that there ARE serious side-effects of getting the vaccine. It's that they think there MIGHT be. Given what we know, we just can't tell.

Even if it doesn’t turn you into a zombie, there is a long history of negative side effects for vaccinations. So, while it’s true that we have pretty good reasons for thinking the COVID vaccine won’t have negative side effects, it’s also true that we don’t have certainty. Compare: I have excellent reason to think it will rain in my hometown at some point in the next three months, but I’m not certain of that. There’s always an outside possibility that I’m wrong. We should be willing to say the same about the COVID vaccine: it’s possible (however unlikely) that there will be terrible long-term consequences of getting the vaccine.

But here’s the kicker: it’s *also* possible (however unlikely) that there are long-term terrible consequences of getting COVID. The science of disease is pretty advanced, and we have good reason to think that most people won’t suffer long-term damage from COVID. But we don’t have certainty. There’s always an outside possibility that we’re wrong, and, in fact, growing evidence that a minority of people will, in fact, suffer long-term effects of COVID. And so, the unknown risks of the disease should be factored into the equation, too.

When we do so, we find that the unknown risks cancel one another out. Worry about the long-term consequences of the vaccine won’t be a reason to avoid it *as long as* there is also worry about the long-term consequences of the disease. Given that, the rational strategy will be the one that maximizes our values given what we know, not what we don’t. And since it’s clear that the most prominent vaccines reduce illnesses requiring hospitalization by 95%, getting the vaccine will maximize expected value for most people.

Here’s another way to make the point. (If you hated high school math, skip the next two paragraphs.) Calculating expected value is a function of probabilities and values. Take an easy case: you drive downtown and need to park your car somewhere. You have only two options. You could either pay $10 to park in an empty parking lot or else park on the street and risk a $50 ticket. You have to pay a machine to get into the lot, but the police patrol the streets only about once every ten days. Assuming your goal is to save money, here’s your expected value for each option:

Strategy | Probability of Loss | Value of Loss | Expected Value |

Lot | 1/1 | -$10 | -$10 |

Street | 1/10 | -$50 | -$5 |

What should you do? Well, if your only goal is to save money (and you don’t care about things like breaking the law), then the expected value calculus shows you that the rational course of action is to park in the street. The odds are good that you’ll lose less money that way.

How does this basic example shed light on the COVID vaccine case? In just this way: suppose as you are parking, someone comes up and challenges you as follows:

"You don't want your car to get stolen, right? And you admit that there's a possibility that it gets stolen if you park it in the street. For that reason, you should park in the lot, instead. The fact that there are potentially unknown negative side effects from parking on the street is a good reason to prefer parking in the lot."

That bit of reasoning shouldn't be persuasive. True, you don’t know the probability of theft when parking on the street. But then again, you also don’t know the probability of theft from the unmonitored lot. In that case, the unknown risks cancel one another out. It would be silly to cite the unknown future risk of car theft as a reason for going with one parking strategy over the other—the risks exist in both cases.

Back to vaccines. The standard anti-vaccination reasoning is that the unknown risks of the vaccine don’t outweigh the risks of the disease. Like the parking case, that’s counting only the unknown risks on one strategy rather than the other. In fact, unless we’re able to assign probabilities and values to the unknown risks (something that we’re unable to do because __it's a big question__), there’s no reason to let the weight of the unknown risks in either direction affect your choice of strategy.

In sum, people who forgo the vaccine because they are worried about unknown side effects of being vaccinated are being irrational. They are ignoring the unknown side effects of getting the disease, and these two unknowns cancel one another out. The rational decision will be the one based on the probabilities that we know and the outcomes that we value. On those numbers, vaccination is the winning strategy.