Vaccination Arithmetic

A good deal of the current discussion of vaccination takes it for granted that it is in almost everyone's interest to get vaccinated, hence that failure to get vaccinated is evidence of false beliefs or irrational behavior. To see why this is not true for everyone, it is worth looking at some numbers.

According to the CDC, the estimated infection fatality rate is 0.05 percent for 18-to-49-year-olds. I start my calculations with someone who is certain to get infected and has a life expectancy of thirty years. Thirty years is 262,800 hours, so the reduction in life expectancy is .0005x262,800=131 hours.

If you believe your chance of getting infected is only .1, not unreasonable if you regard the current wave as the last of the epidemic, that reduces it to 13 hours. If you are 25, which according to one source gives an IFR of .01, that takes it down to less than three hours. Saving that may not be worth the time and trouble of two injections, a likely few days of not very serious side effects and some small risk of more substantial side effects. The same is more true for younger ages or people in particularly good health.

It may be objected that a .1 probability of getting infected is unreasonably low, but that depends what you believe about vaccine effectiveness. If you are optimistic about vaccines, you should expect the current wave to be the last serious one. If you are pessimistic about vaccines, the risk of infection is much higher but the benefit of vaccination lower.

It may also be objected that I am looking only at death. I don't have, I don't think anyone has, good data on long term effects of getting Covid and recovering. The short term effects range from zero for asymptomatic infection to several weeks in the hospital for almost lethal infection. Including that would reduce the number of people for whom vaccination is not a clear benefit but not, I think, to zero. 

And, on the other side, I am ignoring people who have already had Covid, hence have protection comparable to, perhaps better than, that provided by vaccination. Vaccination apparently increases the protection, but not by much. The CDC estimates  that about a third of the population have had symptomatic Covid, so that is a large group for which the benefit should be reduced by at least an order of magnitude.

I am 76, so a similar calculation implies that I should be vaccinated, and I am. But I do not agree with the claim that everyone should obviously be vaccinated as well.

All of this is in terms of the self-interest of the individual. Vaccination also reduces the spread of the disease, benefiting others, although by how much is not clear. That is an additional argument for getting vaccinated but one whose size is harder to estimate.

Am I Irrational

 A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

— Robert Heinlein, Time Enough for Love

In a number of ways my views and acts are difficult to explain as rational. I will list them:

1. As an economist, I believe in division of labor and the benefits of specialization and yet I find Heinlein’s ideal, quoted above, persuasive. I would like to be that sort of person. To the extent that I am — I think I can claim at least thirteen items on his list — I am proud of it.

2. I recently attended a social event, a dinner for forty or fifty people in the host’s home, with catered food. That felt wrong to me. When we host such events, as we occasionally do, almost all of the food, aside from any nibbles brought by the guests, is cooked by me and my family.

3. At this point in my life I am comfortably well off, yet I still make an effort to save money in small ways. We buy flour from Costco in 25 pound bags, pay attention to prices in the grocery store. I look at the right side of the menu as well as the left when deciding what to order. If we eat out, it is usually at relatively inexpensive ethnic restaurants. Looking for a new one, we ignore anything whose online description is $$$. I could afford to fly business class but never do, save for a few times when someone else was paying for it.

4. We do a lot of things in-house that it would arguably make more sense to do through the market. I build our bookcases in my basement workshop. If a button comes off a shirt or a pants seam comes out or the knee of my jeans wears through, my wife fixes it. At any reasonable per hour value for her time, it would usually be cheaper to hire the work out, perhaps to replace the jeans — I get mine from Haband, not L L Bean. But we don’t.

Arguably this is all irrational behavior, perhaps behavior that made sense at an earlier and poorer stage of life, retained through habit.

But perhaps not.

I am comfortably well off at present, but my income reaches me through an elaborate set of social, legal, and political mechanisms and the world is an uncertain place. Quite a lot of Americans who were comfortably well off in 1928 were no longer so in 1930. The same was true a fortiori for French aristocrats in the late 18^th century, Russian in the early 20^th. Even short of stock market collapse or revolution, there are multiple ways in which I could suddenly find myself in a much worse situation, such as a fraud at my broker’s that emptied my portfolio. Any money saved today through habits of thrift would vanish along with everything else, but the habits would not. Even if I am safe through my lifetime, my children extend my concern decades further, and their pattern of life will be in part modeled on mine.

In the world as it now is, most things I want done can be done better and cheaper by someone else, hence it pays to specialize, earn money doing what I am good at, use that money to get other things through the market. That mechanism makes possible for modern-day people a standard of living enormously higher than a self-sufficient homesteading household could produce with its own labor.

The world is an uncertain place. As long as I am alive and without serious injury I have my mind, my hands, my skills. In an uncertain future, there might come a time when I had no access to a market — perhaps not for a day, a month, or, in an extreme case of societal collapse, a lifetime. Modern Americans have lived in a safe world for a very long time, but past performance, as they say, is no guarantee of future returns. There might come a time when I could no longer support myself by teaching, writing, speaking, perhaps a time when I would need to flee my country and find other ways of making a living. Safer not to be a one trick pony.

I conclude that while it makes sense to do most things through the market — I do not grow my own wheat and grind it for flour or spin and weave my own cloth — there is much to be said for maintaining a range of skills, the sort of range Heinlein describes if not his exact list. Just in case.

Insofar as being to some degree a generalist is prudent, it is admirable. Insofar as it is admirable, it is something one feels good about, wishes to demonstrate.  By, for example, feeding forty people out of your kitchen or building your own bookcases.

 

Writing a Novel Backwards

About twenty years ago I wrote Harald, my first novel, started a sequel, decided to work on an unrelated novel instead, wrote a sequel to that, planned a third book in the series. When that project stalled I decided to go back to the abandoned sequel and try to complete it. 

At which point it occurred to me that there was something I should do first. Harald has an implicit backstory, a history of the lands and people before the story starts. To produce a second novel in the same setting I should know that history. 

It was my first novel and it had not occurred to me while writing it that I needed to work out the timeline implied by things characters said, scenes they remembered, bits of dreams. Solving that problem, reconstructing the backstory from fragments of information, felt like historical research — except that the history being researched was fictional. World building, in my experience, feels more like discovery than invention.

I started by going through the book collecting everything in it that had implications for events before the book started, then worked out how to make all of it as nearly consistent as I could manage. It was fun, so I decided to write a blog post about it. 

For example ...

Central to the story is the repeated attempt by an aggressive empire to annex the kingdom of Kaerlia, where most of it happens, four invasions before the book starts, three more during it. Comments by characters imply that the first invasion was  twenty years before the start of the story. Or twenty-five. Or thirty. If I had spotted the inconsistencies before the book was published, as I should have, I would have reduced the disagreements to a more realistic year or two. Since I didn't, I needed to decide what the right number was, interpret the others as careless mistakes. To decide which number to pick ...

My protagonist's grandson appears to be about twelve or thirteen when the story starts. If I assume he was born when his father was eighteen, which is as young as seems plausible, his father would have been conceived about thirty-one years before the story starts. It is clear from details in the text that Harald was not yet married to Gerda at the time of his first battle, probably not for a year or two after, so that battle must have been at least thirty-two years before the story starts. It ended a failed invasion of the empire by the kingdom, so it seems plausible that the first invasion the other way would have been a few years later, putting it about thirty years before the story starts. That also fits the fact that my protagonist, a young adult in his first battle, appears in the book at about the age I was when I wrote it, somewhere in his fifties.

So the first invasion was thirty years before the story starts. Problem solved.

What about the fourth? There are three passages that could all be references to the same battle. One describes Artos, an  important secondary character, as the junior legion commander in a defeated imperial army. By the time we see him he has become the most prominent commander in the empire, which should have taken at least a few years. Another passage implies the death in battle of a woman whose daughter, a young adult, describes someone as sounding like her mother. The context is archery practice, which suggests that she was at least seven or eight before her mother died, which puts the battle she died in at most ten years before the story starts. 

I conclude that all three passages are references to the battle that ended the fourth invasion and that it happened between five and ten years before the opening scene of the book.

Why, for the sequel, do I need the dates of failed invasions? I do not know all the reasons, since I have not written it yet, but I expect parts of the story to involve Belkhan, an imperial province with a history of rebellion. The most recent rising was set off by the Imperial defeat at the end of Harald, which makes it plausible that earlier rebellions were similarly linked to earlier defeats. My objective is to make the whole story, two books, perhaps eventually three, feel like a consistent picture, one where things fit together. 

My main points in this somewhat odd blog post are:

1. I should have done all of this before publishing the novel. So should you if you are writing a novel.

2. But  doing it backwards was fun.