In my last post, I casually brought up masks as an example of a contentious issue, and since I claim this little project is about fostering productive dialogue, I guess that means I have to bat leadoff. So, I will give you my opinion about masks. Please be gentle.
Given the current state of affairs, I almost scrapped this post for being too trite, but since many of us are going out now, and some of us may be going out to protests, demonstrations, outdoor prayer gatherings, and other things, I do think this is still an important topic to tackle. I did want to acknowledge the moment, though; I do plan to write on it soon.
The Classic Argument
The classic argument, as I’ve heard it, appeals to the moral value Care vs. Harm. It goes like this: You are less likely to get the virus or transmit the virus if you are wearing a mask. It doesn’t cost you anything, so you should just do it.
However, the argument has a few shortcomings:
- It does cost something, in terms of liberty, so this argument is not particularly persuasive to people of the liberty vs. oppression ilk.
- It may also have cost in terms of harm to the wearer. If you use it incorrectly, it’s not doing anything other than collecting particles. Moreover, if you trust it too much, you may put yourself at unnecessary risk.
- If we’re talking about cloth masks, there isn’t much data either for or against their usage. That’s different than saying they are useless or negative, but it’s not exactly a glowing endorsement, either.
What I’d like to do here is examine masks objectively and reframe this argument in another way.
A Model for Mask Use
I would try to model masks mathematically, but there are way too many variables to account for. I will limit it to two:
- pi: The probability that, if I encounter the virus, the mask will block me from catching it. Here, i is for inhale.
- pe: The probability that, if I have the virus, the mask will block me from passing it to someone else. Here, e is for exhale.
The reason that I’m doing this is for honesty. If my argument is wrong, then you would be doing me a service by correcting it (cf. Proverbs 9:8), so I am providing you with the channels by which you can offer me correction.
The problem, of course, is that we don’t know the values of either of these two probabilities. However, we may be able to reason about them.
What We Know
- We don’t know pi, but we do know how probabilities behave over time.
If the mask has pi chance of blocking an encounter with the virus, then the probability of blocking the virus after x encounters is pix, since the mask will have to have succeeded in blocking all x encounters. This means the probability of failure (and therefore contracting the virus) is the complement of this quantity— that is 1 – pix. Over time, that looks like this:
I put a horizontal line at 50% because that means that, within the next however many encounters, effectiveness pi implies you’re more likely than not to be infected within the next however many exposures. For example, if the mask is 75% effective, then you’re more likely than not to be infected within the next 2 encounters, but if the mask is 85% effective, you should be able to hold out until 4 encounters.
Using Desmos (online graphing calculator), I put together an interactive version of this graph here. I’ve also put the code I used to generate the above graphs here.
This more likely than not encounter is an important probability concept, and if you just want to compare different values of pi against 50%, the graph looks like this:
The results are highly dependent on the value, but as you can see, even small changes, toward the higher probabilities can make huge differences. So if you end up seeing values for the type of masks you can access, now you can try to visualize what they mean.
2. We don’t know pe, but we know what direction it will push the overall effectiveness.
Since we’re dealing with probabilities both p (chance of a successful block) and 1 – p (chance of a failed block) are between 0 and 1. For a transmission to happen, both masks must fail, which is a smaller chance than one, bringing that at least one of the masks would succeed to 1 – (1 – pi)(1 – pe). It seems obvious, but if we look at the above graphs, we can see that this could make a decent difference in terms of number of exposures you could weather. I’ve made another interactive graph that models what would happen if pi = pe and we have both the sick person and the well person wearing masks; you can see that if the probability of success is just ok, two successes is very good.
I will say, however, we do have reason to believe pe > pi, but even if it’s not, the result of combining the two is significant.
Combination
The takeaway that I want you to have from this exercise is that any effort on this front increases the value for all parties. Look at the curve; as you proceed in any direction (corresponding to either you or the other person increasing their protection level), the value both of you receive is greater than the effectiveness of just your own mask.
Two Arguments for Masks
Having said that, I would now like to propose two arguments for wearing a mask. My goal is to use the above observations and appeal to a moral value other than care vs. harm.
The Libertarian Argument for Masks
I am not a libertarian, but I have many dear friends and family members who are. Since they mean a lot to me, I will try to pose my argument in terms they would hopefully find persuasive. If you are one of those people and are not convinced by this argument, please let me know! I will either improve it or abandon it. Either way, you will have made me better, and for that I will be thankful.
In his second treatise on government, Locke wrote, “Being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions”, providing one formulation of what is known as the Non-aggression principle. You can decide for yourself what is good for you and what is not; others are responsible for doing the same for themselves. If all that is at stake is our own health or comfort, we can decide for ourselves the risk levels we wish to take. If we decide to go outside, that means our preference allows for this level of risk. Aside from that, we should all enjoy the “right to be left alone.” However, if you start infringing on another’s right to the same, that’s when you run into trouble.
Can we rely on people’s going outside to indicate a level of risk acceptance equal to our greater than our own? Because in that case, or in the case of a lower acceptance of risk which results in not coming outside (and thus not risking community virus exposure), you would have no duty to them according to NAP. You’re not violating their wishes at all. However, some people would prefer to be home but must venture to the store to care for sick or vulnerable people, or feed their children. Some others may be comfortable with enough risk to go outside but not unless certain conditions are met. Because these categories are not acceptance of risk, forcing an exposure on them would violate their right to be left alone. Therefore we ought to put a mitigating factor somewhere.
The unfortunate truth about this disease, however, is the fact that many of the infected have no idea of that fact. This makes it at least somewhat prudent to assume that you could carry the virus. But what does that assumption mean for our behavior? If we adhere to NAP, then we should also respect the wishes of others, as we would expect them to do for us.
So can we simply ask those who are more risk averse to wear a mask for themselves? We do not have enough information to conclude that is sufficient. We do not expect pi for cloth masks to be very high, and if pi is less than 50%, then more often than not it will fail on the first encounter. That means if we are an asymptomatic carrier (which we cannot confidently reject) and we encounter someone wearing a cloth mask, we have a very real risk of infringing on their right to be left alone.
I see two ways forward from that. We can either stay away from everyone, or we can try to increase the effectiveness of our protective measures. The only way I can think to do the latter is by wearing a mask ourselves. The combined effect minimizes our risk of infringing on the other person’s right to health, and theirs on our own. It’s still not perfect, but as I showed above, pi < 1 – (1 – pi)(1 – pe), and that difference is significant enough to be meaningful. So I would ask you, if you are going out and cannot reasonably keep your distance, to wear a mask. Otherwise, you could be bringing harm on someone else, and now you’d be doing so knowingly. Is that not an act of aggression?
The Philippian Argument for Masks
I am a Christian, so this one may be easier for me to construct. It is similar to the original argument, but it draws upon Christian ethics and imperatives. Specifically, I will be drawing from second chapter of Paul’s letter to the Philippian church.
The mathematical portion remains mostly the same, but Paul further commands Christians “Do nothing from selfish ambition or conceit, but in humility count others more significant than yourselves. Let each of you look not only to his own interests, but also to the interests of others.” Paul furthermore commands us “do all things without grumbling or disputing” (verse 14). Therefore, if we have reason to believe some action could be harmful (i.e. approaching someone, not knowing we won’t spread to them an illness that could kill them or someone they are caring for), we ought to take on protective measures, and do so joyfully and without complaining.
Final Thoughts
So how was that? I am not an authority on epidemiology (I will write on something more in my wheelhouse soon), so it’s quite possible I’ve made some mistakes. Kindly offer me any corrections you might have. I mean that; if you correct me in good faith, I will accept your correction. I’ll push back if I don’t agree, but I’ll do so respectfully. The end result is that both of us will have helped one another, which is why I started this project in the first place.
Lastly, I hope these realities will not be with us long. It is the specifics of the current pandemic which are imposing these injuries on us. Once there’s either widespread immunity, through vaccinations or otherwise, or if we can reliably know that people are not carrying the virus, the math changes and we can take them off. But until then, please put your mask on if you can.
How to Wear a Mask
Wearing a mask properly is important, since wearing it wrongly would expose yourself to unnecessary risk. Since most of us only have cloth masks at our disposal, I’ve linked to a source explaining how to wear one more effectively.