Ricochet is the best place on the internet to discuss the issues of the day, either through commenting on posts or writing your own for our active and dynamic community in a fully moderated environment. In addition, the Ricochet Audio Network offers over 50 original podcasts with new episodes released every day.
A Question for Mandated-Vaccination Advocates
How are you quantifying the public health risk represented by any given individual not getting vaccinated? Can you give it to me in units of, say, third-party life years lost per year by the decision to remain unvaccinated? Can you give me an estimated probability that the failure of individual X to get vaccinated will result in the COVID death of some individual Y?
No? Can you at least try?
Because you’re giving us a value-of-freedom vs. cost-of-risk inequality that looks something like this:
Freedom < Risk
And I want to know when you think the cost of the risk no longer outweighs our personal freedom to make health care choices for ourselves.
If you can’t give me a number, can you give me a ratio? Can you tell us what relative reduction in risk will drop it below the value you seem to place in individual choice?
Don’t tell me you don’t know. We don’t want to trade our freedom for don’t know.
And it isn’t obvious to me that you’ve got the direction of that inequality right even now. If neither of us knows what the actual risk is, I at least know how much I value individual freedom. So the ball’s in your court and, until you come back with some science and a better argument than I’ve heard, I’m going to assume the freedom I value outweighs the risk you can’t or won’t quantify.
And, until you put a number on it, don’t call it science.
Published in Domestic Policy
They cannot and will not. The fact is, we have no idea how much of a threat someone poses to anyone, vaccinated or not.
What we do know is that those who have had it and those who have had a vaccine seem to get less serious symptoms.
That’s it. You are spot on with this.
I have had more or less the same question about several of the virus transmission mitigation measures imposed in the last 18 months (stay at home orders, “do not gather” orders, business and other entity shutdowns, masks, barriers between people, physical distancing, etc.) – what is a quantifiable measure of the benefits, so we can compare that benefit with the costs (monetary and non-monetary, including social and psychological).
That appears to be true for the original virus, I am not sure that remains true for the combined “alleged” vax risk and the breakthru cases with the variants. I guess that applies to the post. We don’t know, but Henry and I each know, respectively, our value of freedom to opt for or opt against a novel vaccine.
You realize, of course, that’s just asking them to make up a number. Like they’ve done with “climate change.”
That’s something people forget. It’s not just the virus that is “novel,” so are the vaccines.
I’m with you all the way, Henry, but I don’t see how you make this particular argument meaningful with those who put little value, i.e. approaching zero, on personal freedom.
Despite the title, Bob, it isn’t intended for those people. It’s never intended for those people. They aren’t reachable, because they don’t share our values. We write to persuade the persuadable.
Or they assume that only other peoples’ freedom will be infringed, not their own.
The latest data in Massachusetts show that in most towns, the percent of asymptomatic people testing positive on Covid swabs is lower than the false positive rate of the test (3%). So unless someone is symptomatic, there is no value to testing.
It’s over. The pan-DEM-ic is over. The problem is that no one in power will admit this.
I am not a proponent of vaccine mandates. I will take a shot at answering your question anyway, Hank.
I’m not going to put in all of my sources for my various assumptions. I have looked them up briefly, and formed an impression.
I assume that Covid will be endemic, which basically means that you will get it eventually. The Delta variant appears dominant, with an R0 in the 6-7 range. I will use 6.5.
I assume that the vaccine is about 80% effective against symptomatic disease (a factor of 5); that this same factor of 5 governs the reduction in the likelihood that a vaccinated person will spread the disease; that the vaccine is 90% effective against death; and that the vaccination rate is 60%. I assume an infection fatality rate of 0.5% without and 0.05% with vaccination.
If you are unvaccinated: When you get Covid, you will infect 6.5 others, 3.9 vaccinated and 2.6 unvaccinated. The expected number of deaths is 0.0005 among the vaccinated and 0.013 among the unvaccinated. The total number of expected deaths, from the direct infections that you would cause if unvaccinated, is 0.01495.
If you are vaccinated, you will infect 1.3 others, 0.78 vaccinated and 0.52 unvaccinated. The expected number of deaths is 0.0005 among the vaccinated and 0.0026 among the unvaccinated, a total number of deaths from direct infections that you would cause if you were vaccinated of 0.00299.
The reduction in this first-order expected number of deaths, from your vaccination, is 0.01196.
If a life is valued at $8 million, this first-order benefit is worth $95,680. (This is based on the EPA’s central estimate of $7.4 million for a statistical life, in 2006 dollars, which I adjusted up to $8 million to account for 15 years of inflation, without checking the actual inflation figures, which are probably higher.)
The actual benefit from your vaccination would be higher. The math gets tricky here, and I might be able to work it out, but it’s getting late. Basically, if you are unvaccinated, you would infect 2.6 other unvaccinated people, and each of them would cause first-order losses of another $95,680. And so on, and so on.
This compounding effect would diminish, eventually, as either vaccination or further infection causes herd immunity. Effectively, this would change the vaccine coverage ratio in my calculation.
The compounding effect adds up rapidly, though. If you infect 2.6 unvaccinated people, they infect 6.76, and then those infect 17.576, and then those infect 45.6976. After four steps, your infection has spread to 73.6336 other unvaccinated people — each of whom causes first-order losses of $95,680.
This totals a bit over $7 million.
You can tweak those assumptions quite a bit, and still show a pretty big benefit.
I was running out of space, so I want to add a bit. Most importantly, let me know if you see any flaws in my methodology. It seems right to me, but it is getting late.
Frankly, I did not expect the number to end up as big as this calculation showed. Maybe there’s a mistake in it, maybe not. Please check my work.
Also, let me know if you have better information about the various assumptions.
One more thing occurred to me after a few minutes.
In my calculation, the reduction of expected deaths at each level of the calculation was 0.01196. About 87% of this reduction was among the unvaccinated, and about 13% among the vaccinated.
Of the total calculated statistical value of deaths caused by one unvaccinated individual in the first four steps of infection, about $7.07 million, about $6.15 million is due to estimated deaths of the unvaccinated and about $920,000 is due to estimated deaths among the vaccinated.
Jerry, good job. I appreciate your effort.
So, 3.9 and 2.6 represent, respectively, 60% and 40% of the 6.5 secondary infections you suggest would result from an unvaccinated person becoming infected. Those correspond to your estimate of the vaccinated versus unvaccinated population: 60% vs 40%.
So are you saying that vaccination will confer no immunity to infection per se, and that a vaccinated person is as likely to get infected as a non-vaccinated person. Put differently: the vaccine is 0% effective against infection, but 80% effective against symptomatic infection and 90% effective against fatal infection?
The alternative would be that the vaccine confers immunity in 80% (for example) of those exposed, and the remaining 20% become infected but then experience the reduced risk of serious illness or death. Are we confident that that is not the meaning? (My cursory survey of the statistics doesn’t make it clear to me.)
I’d quibble with you about assigning a monetary value, simply because the disease skews heavily toward those nearer end-of-life and so presumably doesn’t represent the average assessed value of life per the EPA — for whatever that’s worth. I’d rather go with life-years lost, but that requires another dimension to your analysis.
In any case, thanks for responding.
PS Presumably some portion of the 40% have already been infected, making them effectively a vaccinated cohort.
Just off the top of my head, I don’t think you can assume such a greatly reduced rate of transmission from the vaccinated. There may or may not be an actual increase in “shedding” among the vaccinated, but it seems pretty clear and obvious that people who don’t feel as sick when they do get it – i.e., the vaccinated – will be more likely to be “out and about” spreading it.
Haven’t we known for over a year that the relative risk is essentially zero?
This.
Just had a look at the Mayo Clinic site for its Massachusetts numbers. The most interesting graph (to me, who am not a numbers wonk, but am a native speaker of English, and pretty fly to what words mean) is the map whose legend reads as follows (emphasis mine):
See, they don’t actually need testing, to tell if it’s (probably) Covid or not, just as long as it keeps the numbers up and the panic alive.
What do you think of this science? https://link.springer.com/content/pdf/10.1007/s10654-021-00808-7.pdf
First paragraph in FINDINGS:
At the country-level, there appears to be no discernable relationship between percentage of population fully vaccinated and new COVID-19 cases in the last 7 days (Fig. 1). In fact, the trend line suggests a marginally positive association such that countries with higher percentage of population fully vaccinated have higher COVID-19 cases per 1 million people. Notably, Israel with over 60% of their population fully vaccinated had the highest COVID-19 cases per 1 million people in the last 7 days. The lack of a meaningful association between percentage population fully vaccinated and new COVID-19 cases is further exemplifed, for instance, by comparison of Iceland and Portugal. Both countries have over 75% of their population fully vaccinated and have more COVID-19 cases per 1 million people than countries such as Vietnam and South Africa that have around 10% of their population fully vaccinated.
I advocate for a long term control group. If everyone is forced to get vaccinated we lose that.
Han, further to your #13.
I had a terminology challenge in describing the vaccinated people who would be affected. I used “infected,” but really meant something more like “were exposed to the extent that they would have been infected if unvaccinated.” I don’t think that this affects the calculation, because the net effect of vaccination on the risk to others is covered by the reduction in their infection fatality rate by a factor of 10, and I didn’t carry out the iterative reinfection calculation among those who would be hypothetically infected despite being vaccinated.
You have a good point about the effect of age on the portion of the calculation dealing with the statistical value of a life. It would be possible, I think, to do a calculation making different assumptions for different age cohorts, but this increases the complexity significantly.
But even if you knock down my preliminary figure by an order of magnitude, it’s still a big number. This is actually causing me to consider re-thinking my opposition to vaccine mandates. I did not think that the effect would be this big, and I did not think that there would be such a substantial effect on the vaccinated, with an estimated 13% of the estimated harm occurring among the vaccinated who, hypothetically, did take action to protect themselves.
The main driver of the large figure is transmissibility. This has an exponential effect on this simplified model. In real life, it wouldn’t actually be exponential, as herd immunity would increase over time, but I only used 4 steps in this calculation, and increases in herd immunity probably wouldn’t be much of an effect over such a short time period. Note that if I went to 5 steps, or 6, the final number would increase substantially.
I would expect that the authorities have much, much better models of this sort of thing. My back-of-the-envelope calculation may illustrate the problem that they faced with the emergence of the delta variant, which would explain the shift in vaccination policy over the summer.
So that you’ll know, I didn’t tweak my assumptions in order to create a large figure. I briefly looked up the relevant figures and made educated guesses about the relevant input variables (like transmissibility and infection fatality rate), without having any idea about whether the final result would be $10 or $100 million.
Finally, I wonder about your overall reaction. You don’t seem to have found a major error in my methodology. I had a thought after posting last night — something like “be careful about throwing down the gauntlet, because someone might pick it up.” :) I was surprised by this result, and wasn’t trying to score points or anything. I find my result quite disturbing.
This.
China Joe yells at the unvaccinated, saying this is a pandemic of the unvaccinated, when in fact, the vaccines have created hundreds of thousands of Typhoid Marys, out spreading the virus unaware.
And all the vaccine mandates are doing is making sure that the pandemic never ends.
Doesn’t matter. joebidenstan told us that if you get COVID your chance of dying is 120% regardless of how many jabs you did or didn’t get.
Worthwhile analysis. The 90% effectiveness against death is about consistent with what I’ve seen, but the death rate varies radically with age, and I believe the infection rate also varies to some extent. And while the 80% effectiveness against symptomatic disease seems about right, based on what I’ve read, the effectiveness against *transmission* (eg, by asymptomatic carriers) sounds high.
a friend of mine who works in the field said the following to me Saturday:
“We don’t really know how it is transmitted”.
That is not an assumption – but a fact. Gavin Newsom and the French Laundry. Nancy Pelosi getting her hair done. The list goes on and on.
Jerry,
I also found your results surprising, and worthy of further thinking and digging. I haven’t done that thinking and digging yet. When I do (and I will), my focus is likely to be on a couple of things: probability of initial infection, relative efficacy of vaccination versus naturally acquired immunity, and the demographics of breakout cases among vaccinated individuals. (We know that vaccination efficacy falls with diminished immune system function, and so is less reliable among the elderly. Does breakout reflect that? What do we know about vaccination efficacy in various cohorts? etc.)
As mentioned previously, I don’t consider a monetary valuation realistic for a couple of reasons. First, most of us aren’t comfortable putting a dollar value on human life (even though I understand the practicality of it from a cost/benefit analysis perspective). Secondly, and more importantly in this case, I think it’s inaccurate given the demographic skew — but we’ve already touched on that.
Perhaps the biggest concern I have regarding your analysis is in the assumption of the initial likelihood of infection. I phrased the question as “life years lost per year” as a result of one individual being unvaccinated. Your response was to project from an initially infected, unvaccinated individual. That doesn’t take into account the probability of that unvaccinated individual becoming infected in any given year, and I’m not sure that the “we’re all likely to get it eventually” observation (which may well be correct) scales well, given that, over time (and perhaps over a relatively short time), R0 will presumably drop as herd immunity grows, both as a result of vaccination and infection.
So, in any given year, I think you’d have to scale all of your numbers by the probability of any particular unvaccinated individual actually becoming infected and contagious. You may have done that, but I don’t think you did.
As it happens, I’m generally pro-vaccination for middle-aged and older adults and those in a high-risk group. I’m strongly leaning toward being anti-vaccination for children, at least given our current lack of experience with the vaccines. But I am strongly anti-mandate, because forced health care is a line I think we cross at our peril (and which we’ve unfortunately crossed before), and I am almost certain that I would accept the consequences of significant increased mortality rather than cross it again.
One other thought: if you are using the R0 number for Delta, about 6.5, then it would be appropriate to also use the severe disease and death rates for that variant, which I believe are lower than for the previous variants.
In your Expected Cost calculation for not being vaccinated, did you the calculation include the life-value-reduction of the individual who decided not to get vaccinated, or did it only include the life-value-reduction for *other* people? A strict libertarian would probably argue that only the second one should be counted when considering mandate policy.
I can’t do numbers. I lean libertarian. I don’t like the mandates. But in principle I am troubled by the fact that I never have had any difficulty with the idea that if your child has not had measles or other such vaxes, you cannot send it to a public school. That always seemed fair to me. Now a school is a tight community unlike the world at large. But the principle remains: you do not HAVE to get yourself out of the possible carrier category, but you cannot expect the rest of us to ignore any danger you may pose.
It is a hard one for me and I am amazed at those who find it so, so simple.
Scott Adams has made the point that the only time people will sacrifice is when they see a clear goal against which progress can be measured. Failing that people will simply do what they prefer to do and make up for themselves whatever reasons they need to justify what they do.
I think many private businesses are opting for a vaccine mandate because it is one of the few remaining forms of discrimination the government, the courts (and the civil rights industry) will let them get away with.
If one of your employees shows up for work not having showered for the last 3 months because he’s an alcoholic who has been drinking a lot of “sauce,” you might be reluctant to fire him for fear of getting sued for discriminating against someone with a disability, alcoholism.
So, if you are a businessman and there are a handful of sub-standard employees you would like to get rid of but your human resources attorneys tell you that you can’t fire, the vaccine mandate is your best bet.
Setting aside the issue of how effective the vaccine is for the moment, I think it is far too difficult for businesses to fire employees these days. So, I hope people will look at these folks getting fired for not getting vaccinated as not so much an argument against vaccine mandates but against most of our anti-discrimination law, which benefits sub-standard employees.
Now, when government mandates a vaccine it’s a bit different.
I wouldn’t – based on empirical evidence.
OK based on this
How did a benefit become a loss?
How does a vaccinated person infect more vaccinated people (0.78 if vaccinated or 3.9 if not) than an unvaccinated person (.52 or 2.6)?
Additionally, since the probability of death is the same among both groups (vax and unvax) – and vaccinated people are more susceptible getting the disease (.78 or 3.9 depending on the source compared with .56 or 2.6) then what again is the benefit of the vax given community spread?
The rest of the math is not yet making sense to me, so I am working on a spreadsheet.