Risk Tolerance, Risk Aversion, and the Vaccines

I first encountered these terms, “risk aversion” and “risk tolerance,” in a mathematics class, but to my disappointment, it was just a brief sidebar in the book. I think the concept is fascinating. Of course it has different imports in a variety of areas, such as probability theory, gambling, stock investing, or just daily subjective “decision tree:” choices.

I am sure that experts in any of these fields would have a more precise understanding of the advanced mathematics part of it. But I certainly understand the concept: that people vary in their appetite for, or fear of, taking a risk.

Obviously, it depends on what you are risking, what the reward is, and what the penalty for being wrong is. Let’s look at a rather benign gambling example. Let’s assume you are dealing with a fair coin, and a legitimate device which flips the coin high in the air, turning over a few times until it comes down. Another person tells you that if the next toss comes up heads, he will pay you $5, and if it comes up tails, you will pay him $3. Most people would take that bet, you are getting 5 to 3 odds on a perfectly even proposition. If this were played a thousand times, the odds are that the results would be fairly close to 500 heads and 500 tails, so you would take in $2,500 and pay out $1,500, and you would net $1,000. Even if the results varied to where it was maybe only 480 heads and 520 tails, you would win $840. Any reasonable person would take a bet like that.

Now, if this were only flipped once, would you still take it? Probably; the odds of 50-50 are still the same but of course probabilities play out over a larger sample. But it is still a good deal., and of course you are only risking $3.

What if he said that he would pay you $500 if it came up heads, and you would pay him $300 if it came up tails. Would you do it? Many would not, because even though the odds are very positive for you, if there is only one flip, you have a 50-50 chance to lose, and $300 is a lot of money. If it were flipped a thousand times, and no one had to pay until the flipping was completed, you probably would do it, because the odds are very large that you would win money. Even if it somehow came up 600 tails to 400 heads, which is virtually impossible with a fair coin, you would win $20,000. If it came up 500 each way, you would win $100,000.

But what if the bet were, you get $5,000 for heads and you pay $3,000 for tails, and only one flip? Most would not do that, though a professional gambler would, or someone with a lot of money. Of course, this begs the question as to why someone would give you such a great gamble, but we will ignore that for these purposes, and just assume that the other person is a wild gambler. The point here is, that there is a level at which a person will opt out of the risk, even if it is in his favor, because the cost of losing is too great.

We can test this for each person, by simply asking him or her which bets they would take, and which they wouldn’t. At $5 to $3, and only one flip, almost everybody would, At $50 to $30, and one flip, many would. At $500 to $300, many would not, and so on. One could derive a graph of a person’s tolerance for, or aversion to, risk, as the amount risked increases. It does vary with people, in many aspects of life.

Those are mathematical examples, where the probabilities can be calculated. In other areas, they are more subjective, and so one has to try to make the best guess as to the probabilities, and the risks of good or bad outcomes. But you cannot actually verify them, and so your calculations are susceptible to misperceptions, positive or negative biases, and speculations. Humans are not machines. Even so, we make subjective mental calculations all the time, trying to figure out the relative risks and rewards for choosing among various alternatives.

Back to the more mathematical decisions, we have poker, sports betting, stock market investing/gambling, where we must make the best probability assessments we can. Hopefully, people who do this have a certain level of risk aversion at the higher stakes. Betting your life savings on a hand or a game or a stock buy, is never the right thing to do, even if you think the odds are significantly in your favor. Now, there are some gamblers who will indeed wager immense sums when they think they have the edge, but that is not the vast majority of people.

That was just a little background on the concept of risk, which I thought that you might find interesting. Now, to move to the immediate and crucial matter where this comes into play, Riverdaughter just wrote about us learning that the Johnson & Johnson Covid vaccine has been found to be connected to a rare and severe type of blood clot, so far in six persons, out of all those vaccinated with that vaccine. RD estimated this at .0001%, or one out of a million, which certainly seems accurate. Of course, that is only based on the data so far, but there have been many vaccinated, so that the probability percentage should be pretty reliable.

So what is the decision tree for assessing whether you should get this vaccine? I can understand someone wanting a different vaccine, but that may not be possible right now. If your only choice is to get the J&J vaccine, or not to get any vaccine, what is your positive result vs. negative result choice? You could get a blood clot, which is very dangerous. But the odds are so small, though not nonexistent. If you don’t get the vaccine, you have a much higher risk of getting Covid, and that risk may go higher as the variants get worse. So it would seem obvious.

But I am not making the decision. I have gotten two shots of the Pfizer vaccine. I am not an unvaccinated person making the choice, and it is always easier for someone to decide for other people. But If I had not been vaccinated, I would try to get one of the other vaccines. If I simply could not, I would take the risk of this vaccine. If it is pulled off the market until more data comes in, that is understandable, and the choice has been made for people’s protection, because there are other alternatives. The worst choice for anyone to make in this calculation, is not getting vaccinated,

Each risk choice comes with a different set of circumstances and significance. It would make little sense to use the same analysis in each situation, and there is the very important question as to whether the risk is yours alone, or you are putting other people at risk. There is a lovely museum near me, the Getty Museum. The only issue is that to get up there from the parking lot, you have to take a tram up the winding mountain road, which takes you around the edges of the mountainside. The trip is about two minutes. I am uneasy around heights, particularly where cliffs are concerned. I know that there has never been an accident on this tram, but I was very hesitant to do it. Interestingly, when they had reopened the downtown Angels Flight tram ride up the steep hill to the restaurant, I remarked to a colleague as we walked by it, that I would still not be eager to go up there, and she agreed; and then a fairly short time later, there was a fatal accident on it, and they closed it down again; I did not follow whether they redid it again, or gave up. So there are never no risks.

Of course, if I did not choose to take the tram ride to the Getty, all I would lose would be the chance to see great art. The exhibit that I wanted to see was a rare JMW Turner collection, and he is my favorite artist, so I did it–but I walked down the hill to get back to the parking lot; once was enough of going around the cliff edge! But I would be very unusual in that regard, and of course I had choices, and whatever I chose would not risk others.

With regard to the J&J vaccine, there seems to be a much worse risk if you do not get the vaccine. But again, this becomes a perceptual thing. We know that there are millions of Americans who are refusing to get any vaccine, which seems incredible, but we know the reasons for it. Such people are going to use the J&J information to validate their refusal to be vaccinated, which is very bad for the population as a whole. Even worse, they are going to use it to proselytize others not to be vaccinated.

This is where probability calculations; risk tolerance vs. risk aversion, become more complicated.. One’s decision about whether to get vaccinated or not, is not just going to affect that person’s health, it very well may also affect the health of many people, maybe even everyone. More variants are originating, and we do not know if we can stop all of them with the vaccines we have. And others will arise, if too many people are not immune through vaccination. If the virus keeps being passed among tens of millions of unvaccinated people, there will likely be a series of variants, and we may get one which is far scarier than even the original form. It is imperative for all countries to have everyone vaccinated, or at least as close to that as possible.

So it is not just about real probabilities, but people’s perception of them, and how those affect other people. We all take various risks, hopefully not too high; but every time we get in a car, we do, and there are other things we do which carry some short-term or long-term risk. This particular choice is one of those where one person cannot just accept the personal consequences of his or her decision, there is unquestionably a more widespread effect.

The question of whether a society thus has the right to protect its citizens through the use of health protocols and even mandates, seems both crucial and established. I would be inclined to want there to be a government order for everyone to be vaccinated, but of course that would never be accepted in this country, where freedom now seems to include the right to risk everyone’s health or safety, to suit one’s own preferences. Should any one person get to possibly choose the entire society’s collective risk, if his calculations are simply self-indulgent and wrong?