The scene: Ancient Athens. Glaucon is standing in the Parthenon, wearing a face mask. Socrates enters with his face fully visible.
Socrates: Greetings, Glaucon! How fare you during this awful plague?
Glaucon: [jumps 5 feet] What the hell are you doing? Are you trying to kill me?
Socrates: No, why would you think so?
Glaucon: We’re indoors and you’re not wearing your mask!
Socrates: I’m 20 feet away from you. And the Parthenon is cavernous.
Glaucon: You should be wearing a mask.
Socrates: Very well. [dons mask] Feel safe enough to talk now?
Glaucon: [unconvincingly] Sure.
Socrates: I suggest we go outside to continue the conversation with greater ease.
[One minute later, outside the Parthenon; Socrates and Glaucon are 25 feet apart.]
Socrates: I must admit, Glaucon, I’m very puzzled.
Glaucon: About what?
Socrates: About your level of fear.
Glaucon: [with trepidation] Oh, I’m not afraid.
Socrates: Well, what do you think are the odds that I’ve got the plague right now?
Glaucon: Uh, one in a thousand?
Socrates: Reasonable enough; I’m asymptomatic after all. Now, supposing I was sick, what are the odds that I would have infected you within the Parthenon while wearing a mask?
Glaucon: One in twenty?
Socrates: Plausibly. And what are the odds I would have infected you in the same scenario without wearing a mask?
Glaucon: One in five?
Socrates: Very well. Now as we both know, susceptibility to the plague depends heavily on age and underlying conditions. We’re both fifty. Do you have any underlying conditions?
Glaucon: Thankfully, no.
Socrates: Then according to a table Plato compiled for me, your odds of death if infected are about 1 in 2000.
Glaucon: It’s not just about the risk of death, Socrates!
Socrates: It never is. There is also the unpleasantness of the plague’s symptoms, and a small chance of long-run harm. Still, the same goes for almost all risks. Those who survive a fall from a horse usually suffer pain for a week or two – and a small fraction are maimed for life. So we can still fruitfully compare your risk of death from plague to other mortality risks, never losing sight of the fact that death is only one of many possible tragic outcomes.
Glaucon: [nervously] Fine.
Socrates: Very well, let us calculate the risk I imposed on you earlier by not wearing a mask. We multiply my risk of infection times the change in your infection risk times your mortality risk. That comes to 1/1000 * (.2-.05)* 1/2000, which rounds to about 1-in-13 million.
Glaucon: And that seems small to you.
Socrates: Wouldn’t it seem small to any sober man?
Glaucon: Well, is it really so awful to wear a mask?
Socrates: I wouldn’t mind if the numbers were more favorable. If I were endangering a thousand people like you, I’d happily wear the mask. As it stands, though, your fear seems paranoid and your outrage seems unjust.
Glaucon: Look, why should I have to endure any risk for your comfort?
Socrates: You’re enduring a risk right now. Surely you don’t imagine that your infection risk magically falls to zero as soon as you exit the Parthenon?
Glaucon: Well, why should I have to endure an unnecessary risk?
Socrates: It is “necessary” that we speak at all? Hardly. And we could slash our risk further by separating a hundred feet and shouting at each other.
Glaucon: Now you’re just being difficult.
Socrates: I only wish to understand you, Glaucon. Is that your horse over there?
Glaucon: Yes, Pegasus is his name.
Socrates: A noble moniker. Now do you know the annual risk of dying on horseback?
Glaucon: About one in ten thousand?
Socrates: Indeed. Yet you’ve never fretted over the risk of death by horse?
Glaucon: The daily risk is 1/365th the annual risk, or hadn’t you considered that?
Socrates: Quite right. The daily risk of death by horse is therefore about 1-in-4 million – more than three times the risk that terrified you inside the Parthenon.
Glaucon: As long as I’m alone, I’m not exposed to any risk of plague at all.
Socrates: And as long as you’re unhorsed, you’re not exposed to any risk of death on horseback. Yet during the minutes you’re on horseback, you’re a model of composure. Why then are you so fearful of plague?
Glaucon: Plague is contagious. Death on horseback is not.
Socrates: I’ve seen you riding with your son, slightly endangering his life as well as your own. That’s not precisely “contagion,” but you can hardly claim that you’re endangering no one but yourself when you ride Pegasus.
Glaucon: If I catch plague, though, I could be responsible for the deaths of thousands.
Socrates: Possible, I’ll grant. If you were returning home from a plague-infested land, I’d understand your scruples. You wouldn’t want to be the conduit for mass destruction.
Glaucon: Indeed not.
Socrates: By now, however, this plague is already well-advanced. You’re highly unlikely to make it noticeably worse. Indeed, by this point the average person infects less than one extra person.
Glaucon: I might not be average.
Socrates: You are right to say so. Still, shouldn’t our knowledge of averages guide our behavior? In any case, let us return to the key issue: Why are you so fearful of talking inside the Parthenon without masks when the risk of death is vanishingly low?
Glaucon: Perhaps we should sponsor a raging Bacchanalia, then?
Socrates: I think not. A drunken festival of a hundred people would probably have a thousand times the plague risk of a two-person conversation. We should avoid that until the plague subsides.
Glaucon: So you admit the danger?
Socrates: I always did. I’m not saying that plague is harmless. I’m saying that you’re reacting to risk qualitatively rather than quantitatively.
Glaucon: Meaning?
Socrates: You’re much more afraid of a tiny plague risk than a larger horseback risk. Why do you think that is?
Glaucon: Have you ever seen someone die of plague?
Socrates: Have you ever seen someone die on horseback? Both are terrible tragedies, with a long list of ugly secondary risks.
Glaucon: Look, you’re in denial. Everyone in Athens is scared of the plague. Your risk analysis is beside the point.
Socrates: How can risk analysis ever be “beside the point”?
Glaucon: We as a society have decided to fight the plague, and you’re going to have to do your part, like it or not.
Socrates: Glaucon, what is my profession?
Glaucon: What?
Socrates: I said, “Glaucon, what is my profession?”
Glaucon: You’re a philosopher.
Socrates: Indeed. As as a philosopher, what is my mission?
Glaucon: To defy and aggravate others?
Socrates: Hardly. As a philosopher, my mission is to improve the thinking of my fellow Athenians, my fellow Greeks, my fellow human beings.
Glaucon: [sarcastically] Very noble.
Socrates: I take a certain pride in my efforts. How, though, am I supposed to improve their thinking?
Glaucon: I don’t know.
Socrates: The answer, seemingly, is: By asking questions.
Glaucon: [weary] Yes, yes.
Socrates: Now Glaucon, when you urge me to “do my part,” what do you have in mind?
Glaucon: Wear the mask, Socrates.
Socrates: I’m wearing one now, to put you at ease while we converse. In more crowded conditions, I’ve worn a mask out of prudence and decency. But as a philosopher, obediently wearing a mask is woefully inadequate.
Glaucon: Well, what more should we do?
Socrates: I don’t know about non-philosophers. For we philosophers to “do our part,” however, requires us to challenge popular fallacies and innumeracy.
Glaucon: Isn’t this just an elaborate rationalization for putting your own comfort above the lives of your fellow Athenians?
Socrates: Possibly. More likely, though, your agitation is an elaborate rationalization for putting conformity above reason.
Glaucon: Your numbers could be wrong, you know.
Socrates: Indeed, I suspect that all of my numbers are wrong. As we learn more, each of my numbers will be revised.
Glaucon: If you don’t really know the risks, why are you lecturing me?
Socrates: Because, Glaucon, you’re approaching the uncertainty emotionally rather than analytically. Uncertainty is a poor argument for panic.
Glaucon: I was never “panicked.”
Socrates: Very well, let us take off these masks, re-enter the Parthenon, and continue the conversation in comfort. The midday sun is too much for me.
Glaucon: Are you crazy, Socrates?
Socrates: And a corruptor of the youth, from what I hear. Do you think there will be a trial?
Glaucon: Look who’s panicking now!
Socrates: A fair point, my dear Glaucon. A fair point.
Glaucon: Look Socrates, it all comes down to this: There’s no reason not to just go along with society’s expectations here.
Socrates: No reason? What about friendship?
Glaucon: I don’t follow you, Socrates.
Socrates: Since this plague struck, I’ve barely seen you. Mask or no mask, you avoid me, as you avoid almost all human contact.
Glaucon: Well, what do you expect me to do?
Socrates: Weigh the tiny risks to health against the immense value of friendship.
Glaucon: You’re making too much of this, Socrates.
Socrates: Am I? The great Epicurus taught us that friendship is one of the highest of goods. Friendship is essential to human happiness, and a life well-lived.
Glaucon: You speak unjustly to me, Socrates. I am and ever have been your friend.
Socrates: I know, which is why your panic pains me so.
Glaucon: If you’re really my friend, you will share my concern for my own safety.
Socrates: I do, Glaucon. If you were in serious danger, and I could save you by shunning you, I would grieve. Yet shun you I would.
Glaucon: Very gracious of you.
Socrates: I know you would do the same for me.
Glaucon: Again, most gracious.
Socrates: The plain fact, however, is that you are not in serious danger. By the numbers, you are in the kind of minor danger that you’ve always accepted in the past.
Glaucon: And?
Socrates: And so I say the time is long since past to resume our normal friendly relations. In troubled times, minor adjustments are often wise. But abandoning your friends out of fear of minor risks is folly, Glaucon.
Glaucon: [forced] Well, thank you for your candor, Socrates.
Socrates: [resigned] May we meet again in saner times, my friend.
Glaucon: Good day to you, Socrates. Good day.
[Glaucon and Socrates go their separate ways.]
READER COMMENTS
Spire
Sep 8 2020 at 10:57am
“Socrates: Quite right. The daily risk of death by horse is therefore about 1-in-4 million – less than one-third of the risk that terrified you inside the Parthenon.”
Not sure if typo, but should this not read “three times the risk” rather than “one-third the risk”?
Bryan Caplan
Sep 8 2020 at 7:56pm
Thanks!
Thomas
Sep 8 2020 at 5:05pm
Ah, but had Socrates recently visited the Piraeus?
Daniel Klein
Sep 8 2020 at 7:13pm
Great piece. Great.
A lot of confusion these days. The scene overflows with denial.
Phil H
Sep 8 2020 at 10:16pm
“Well, what do you expect me to do?/Weigh the tiny risks to health against the immense value of friendship.”
A Peter Singer-style argument that doesn’t seem to work very well with people. I don’t feel like I have the necessary knowledge or the time to do all this weighing. Whereas I do understand the social norms around me, and I’m willing to follow them. The person putting the argument (Socrates/Caplan) should put themselves in the position of the audience. All of a sudden, an interlocutor (Caplan) demands that I act in a spectacularly rational way in one particular area of my life. I know that I don’t do that in most areas. And I’m pretty confident that Socrates/Caplan doesn’t do it in all areas of his life, either. So I feel put-upon, and I wonder if all this isn’t just a bit self-serving. (Because that’s what human interaction is like – it’s not a comment on Caplan’s character.)
nobody.really
Sep 9 2020 at 9:55am
Glaucon: Isn’t this just an elaborate rationalization for putting your own comfort above the lives of your fellow Athenians?
Socrates: Possibly. More likely, though, your agitation is an elaborate rationalization for putting conformity above reason.
Glaucon: Indeed. And as we observe throughout the world, people tend to conformity. Perhaps we should attach no significance to this practice. But if we acknowledge the existence of positive and negative feedback loops, we may imagine that harmful conformity tends to die out while helpful (or at least not very harmful) conformity tends to endure. Thus, I find it rational to conform. You, like the French philosophers, embrace radical rationality with a hubristic faith that you can anticipate all the consequences. I, like Edmund Burke and H.L. Menken, embrace the idea of conformity, even as I acknowledge that I don’t fully understand the reasons for every practice to which I conform.
Socrates: Wait—we’re talking about conforming to a practice that is only a few months old.
Glaucon: True, those are not especially time-honored practices. But from the perspective of Burke and Menken (who won’t be born for millennia), those practices are ancient.
Socrates: Now you’re just being silly.
Glaucon: Fair enough. But I do have a point: Mindless conformity reflects a REAL STRATEGY for coping with uncertainty. Rationality reflects another, and often better, strategy—but a costly one. Daniel Kahneman would characterize the difference as Type One and Type Two thinking—and observe that Type One thinking dominates human behavior. So let us imagine that you do not persuade me. We go our separate ways, forsaking opportunities for friendship for now. I acknowledge this cost. Alternatively, let us imagine that you DO persuade me. We reject our masks and enjoy ourselves. You are a famous man. Many will observe us. Because of mindless conformity, many will be motivated to shed their own masks, even under circumstances that you and I would agree do NOT justify it. Yet this is the nature of conformity—it’s mindless. The fact that you and I might be able to articulate with precision exactly when and when not to wear masks will prove unavailing to the vast majority of people who see us but never have the opportunity to enjoy this lengthy discourse on probabilities. I could well imagine that your hyper-rational policy would result in a worse outcome than my knee-jerk conformity.
In short, you do us a favor by identifying hypothetical optimal policies. But REAL public policy requires not merely identifying optimal policy, but identifying how to get the public to embrace that policy—and know when to stop. We establish a minimum age for driver’s licenses not because NO 14-yr-olds could safely operate a motor vehicle, but because we judge that many couldn’t, and a bright-line test is easier to administer and for the public to understand.
Socrates: You know, perhaps you should get tested again. I need to tell you, friend, you’re raving.
Glaucon: I get that a lot.
Phil H
Sep 9 2020 at 10:08pm
It took me a while to wade through, but yes! That’s exactly what I was saying.
Joseph Hertzlinger
Sep 9 2020 at 1:30am
Marcus Aurelius, on the other hand, refused to see Commodus while ill…
River (Frank) Bellamy
Sep 9 2020 at 1:38am
Seeing Socrates and Glaucon talk about quantifying risk with numbers is like seeing them talk to each other on cell phones – the technology won’t be invented for another couple of millennia, it is very much out of context in this historical setting.
It also comes off as out of character to me. For me, Socrates, and philosophy as a discipline, represents the folly of trying to reason without data and with imprecise human language. If you put Socrates in a room with Bayes, for example, I imagine Socrates dismissing everything Bayes says about probabilities with questions like “but isn’t it possible” that fail to grapple with the more rigorous quantitative reasoning. But I guess other people associate different things with Socrates. If he lived at all, he lived long before probability theory existed, in a poorly documented historical era, so the question of how he would have responded is possibly not well defined and definitely impossible for us to know.
Liam
Sep 9 2020 at 10:32am
It’s not historical fiction, it’s just a fun parable in the style of a Socratic dialogue.
Alexander Turok
Sep 10 2020 at 12:14am
If you don’t understand the idea of caring about spreading it to other people for whom the risk is much greater, all this mask-wearing does seem irrational. I get that some people are so fat it’s hard to breathe without a mask and even more of a struggle with one, but it’s really a minor inconvenience in the grand scheme of things. Bryan’s not fat, so I really don’t understand his objection.
anon85
Sep 10 2020 at 4:05am
There are several mistakes in this post; when you accuse others of innumeracy, it behooves you to check your math.
The most glaring mistake is this:
Let’s do the math, shall we? According to one of the best COVID-19 models, the R_t in the US hovers around 1 or a bit below depending on the state. Let’s assume R_t=0.9. If I get COVID, how many people will I infect, on average? The answer is 0.9 the first round, but each of them will infect an additional 0.9 people, so that’s 0.81 in the second round. Then 0.9^3 in the third round, and 0.9^4 in the fourth round, and so on. When all is said and done, I’ll be responsible for 1/(1-R_t) extra infections, which is 10, not 0.9, when R_t=0.9.
Socrates cannot assume those extra infections have the same age as him. He must go by the overall IFR, which is around 1 in 200 chance of death. 1 in 200 for 10 people is 5% chance of killing someone (assuming an infection occurred during that conversation). This is off by a factor of 100 from what Socrates was implicitly assuming! (He was using 1 in 2000 chance of death if the conversation lead to an infection.)
robc
Sep 10 2020 at 9:30am
Your math is wrong. Person A is only responsible for the first generation of infection, so .9 is correct.
The person they infect, or .9 of a person, is responsible for the next generation, and so on. You can’t count the entire chain as the initial person’s responsibility or you are double counting. Unless you think the ONLY person with any responsibility is patient zero.
Also, you don’t have to go by the IFR if you are avoiding high risk groups, which Socrates specifically referred to, as you are only responsible for that first generation. If you are partying with college kids, you have almost zero responsibility, based on the 26k infections across 29 major universities resulting in zero hospitalizations so far.
anon85
Sep 10 2020 at 5:46pm
Some of the subsequent infections are impossible to prevent. For example, people who share a household usually cannot avoid infecting each other (unless they know in advance to separate, but people generally don’t know as they are asymptomatic at first). Household infections are a large driver of the epidemic. Also, many types of essential workers cannot avoid going to work.
Instead of trying to assign blame, let’s consider the policymaker’s point of view. You’re a policy member charged with trying to maximize welfare. Do you mandate mask wearing between Socrates and Glaucon, or not? You could, of course, mandate mask-wearing in other gatherings, as Socrates suggested. But you cannot prevent household infections or infections for essential workers. Arguably, you cannot even prevent assholes from not wearing masks in larger gatherings.
Given these constraints, you know that R_t=0.9 is all you can achieve for society at large. Now consider Socrates and Glaucon. Do you mandate that they wear a mask? The answer should probably be yes, because if one infects the other, the infection will spread to an expected 10 other people, and not all of them will be young, just like I said.
Alexander Turok
Sep 11 2020 at 12:22am
It’s double-counting in the same way as if two people jointly commit a crime, they can both be held responsible for that crime. If you jointly kill someone with a co-conspirator you don’t get half the sentence.
robc
Sep 11 2020 at 8:30am
Although when someone kills two people they are sentenced to two terms (although sometimes concurrently instead of consecutively) so maybe we should split the sentence for a joint murder. It would make as much sense as doubling the sentence for a double murder.
When a mob of 100 people kill a person, it is rare (never?) for the entire mob to get life sentences. So we are already dividing responsibility. Maybe it should be more formal?
nobody.really
Sep 11 2020 at 12:03pm
Video shows a prison guard fainting in a prison yard. The uniformed prisoners huddle. One of them emerges from the huddle and wanders off camera. The rest attack the guard, killing him, but the video is not sufficiently distinct to reveal their identities. All the prisoners in the yard are charged with murder. What result at trial?
1: All acquitted. Prosecution cannot prove beyond a reasonable doubt that any given prisoner isn’t the prisoner who wandered away.
2: Potentially all convicted but one. The prosecution merely needs to get one of the prisoners to make a self-serving statement that he did not participate in the attack on guard, and can then introduce that statement in the prosecution cases against all the other prisoners. If multiple prisoners make such self-serving statements, the prosecution can pick from among them. Heck, the prosecution could hold auditions to see which of them would make a more convincing witness in testifying against the others.
This variation on the Prisoner’s Dilemma illustrates the fragility of the concept of reasonable doubt: Enormous statistical evidence of guilt is deemed insufficient to overcome the doubt. But even the most blatantly self-interested (and likely false) statement can be judged sufficient.
nobody.really
Sep 11 2020 at 10:51am
I know of no mathematical concept of “responsible for,” or causation generally. I sense people here are expressing different views, but I wouldn’t characterize those differences as resulting from math errors.
robc
Sep 11 2020 at 11:52am
Sure there is, its the entire basis of multi level marketing. I am not sure if that is an argument for or against my position.
nobody.really
Sep 12 2020 at 12:46am
🙂
Adam Michalik
Sep 10 2020 at 2:05pm
Great post. We need more sanity and less panic in our society, that’s for sure.
I have a complaint about your probability calculations:
> The daily risk is 1/365th the annual risk.
That’s not quite true. Let p be the probability of fatal accident in a given day. Then the probability of no fatal accident is of course 1-p, and if we assume the probabilities of accidents in all days are equal and independent, the probability of no accident in one year is (1-p)^365, and so probability of fatal accident in a year is 1-(1-p)^365, which is not 365*p. However, for small p, it’s pretty close, so it doesn’t change the argument significantly.
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