The Principle of Two Errors

A couple of years ago, my friend Joel began to lose his eyesight. It was really minor at first, and the vision-loss was gradual. For the first couple of months, his eyesight was not much worse than yours or mine, so it was perfectly safe for him to keep driving. But as his eyesight continued to diminish, it became clear that someday soon he’d have to give up driving for good.

Joel was navigating a very difficult and scary period in his life. Unsure of what to do, he asked me for advice. We talked about how, after life-changing events like becoming paralyzed, people prove to be psychologically resilient: A couple of years down the line, they wind about as happy as they were before.¹ We talked about how he could continue to succeed in his career as a pub owner, with adjustments, of course. And then the question of driving came up. When should he quit?

I thought about it for a while, and then asked him this: “Joel, would you rather quit driving too soon, or too late?”

Normally, when we make decisions, our goal is to be right. But this way of thinking often fails us. So instead, I framed the decision in terms of the two ways he could be wrong: He could either switch to Ubers and Lyfts sooner than he needed to, or he could keep driving past the point where it was safe and get in an accident. He drove home from our meeting that day and never drove again.

The method I used to help Joel with his decision is a technique I call the principle of two errors.

The Principle of Two Errors

This decision-making tool is based on three premises:

1. Anytime we’re faced with a decision, there is always the possibility of being wrong because we can’t predict the future.
2. If we’re choosing between two options, then there are two ways to be wrong.
3. Often, one of those errors is high-likelihood and low-cost, while the other error is low-likelihood and high-cost.

Let’s use what I consider to be an easy decision to illustrate: the choice of whether or not to wear a bicycle helmet.

If I want to go for a bike ride, I can either wear a helmet or not: two options. And on my bike ride, I will either crash – thus needing the helmet – or I won’t. So I could make the error of wearing my helmet when I don’t need it, or I could make the error of not wearing it when I do need it: two possible errors.

The vast majority of the time I ride, I don’t need a helmet because I don’t crash. Therefore, if I choose to wear a helmet, I’ll usually be wrong. The cost of this error is small: just the bit of time it takes to put on and take off my helmet, maybe a little discomfort, maybe it messes up my hair, and maybe I’d prefer to feel the wind blow through my hair as I ride. But on the rare occasions when I’m right – that is, when I crash – my helmet will give me an enormous benefit; it might even save my life.

On the other hand, if I don’t wear a helmet, I’ll usually be right because I usually don’t need it. And every time I’m right, I get a little benefit: a little time saved, the feeling of wind rushing through my hair, etc. But the costs of being wrong are potentially catastrophic. If I have a bad crash with no helmet, I could die.

Here’s a chart laying out the four possible outcomes. The two errors are in bold.

So the way I make this decision is by considering the cost of the two errors: needlessly wearing a helmet or spilling my brains on the pavement. Although the likelihood of the second error is tremendously low, I simply cannot afford to pay that cost, so I always wear my helmet.

Complications

As the cost of the high-likelihood error goes up, the decision gets more difficult. The cost of putting on a bicycle helmet is negligible. The cost of a low-deductible health insurance plan is not.

Furthermore, humans are notoriously bad at probabilistic thinking,² and it might be impossible to know what the odds are in the first place. We sometimes make the mistake of thinking that rare events never actually happen. As a result, we’re frequently overconfident and underprepared. But, as Nassim Taleb famously pointed out in The Black Swan, while rare catastrophes are very unlikely in the short-run, they are almost inevitable in the long-run.³ Sometimes the stock market crashes; sometimes we crash our bikes.

In the face of these difficulties, the principle of two errors can help you make better decisions. The point isn’t that you should always choose the high-probability, low-cost error, but that you should think about difficult choices through this lens. Rather than asking yourself which option is right, you should ask yourself whether or not you can afford to be wrong.

Applications

Now let’s apply this decision-making tool to a series of increasingly difficult decisions.

What time should I leave?

Imagine you have to drive to work, and the drive normally takes 30 minutes, and let’s say you’re deciding between allotting 30 minutes for the drive or 40 minutes.

If you plan on a 30-minute commute, you’ll usually be correct, and you’ll arrive right on time. But once in a while, some unexpected bit of traffic will make you late. On the other hand, if you plan on a 40-minute commute, you’ll usually be wrong, and you’ll arrive 10 minutes early. But on those days when you hit unexpected traffic, you won’t be late. So there are two ways to be wrong: being early or being late.

There’s no universal “right” answer to this decision – it depends on the job you have. At my job, I have a rigid schedule of appointments, back-to-back, so being late throws off the entire day. Of the two errors – being early and being late – I would rather pay the former. Plus, I prefer the lower-stress and higher-resiliency that comes from having slack.

But if your job doesn’t care if you’re occasionally a bit late, and if ten minutes longer at home means ten more minutes with your family, you might choose differently.

Notice how, if the consequences of being late to something go up, you’re more likely to budget extra time. If you’re flying to Austin for an important business meeting, and you get to the airport late, you might miss your flight and miss your meeting. In that case, you’ll probably leave home early and resign yourself to waiting around at the airport for a while. Better not to risk it.

Procrastination

If you’ve got a project to do, and the deadline isn’t soon, you’ll most likely be tempted to procrastinate. And most of the time you’ll get away with it: You’ll be able to get it done at the last minute. But there’s always the risk that some unforeseen obstacle will come up and prevent you from finishing it on time. On the other hand, if you plan to get it done early, and something goes wrong, you’ll have time to fix it before the deadline.

So, when you’re tempted to put something off, and you think to yourself, I’ll have time to do it later, consider what the consequences will be if you don’t. If you can’t afford to pay that cost, then you can’t afford to take the risk of procrastinating.

Risky Behavior

When I was younger, I regularly skied in “no-fall zones” – places where, if you fall, you might die. In general, this means skiing along the edge of a cliff. But I never worried about it because, for the most part, I never fell. And, since most people don’t ski there, you can get fresh tracks.

But one cold, February afternoon, while skiing along the edge of a 30-foot cliff, I fell. Luckily (and obviously since I’m writing this) I didn’t die. But I did injure my back and my knee, and I’ll probably have pain and limitations for the rest of my life because of it.

I also scared the shit out of myself. I realized that I can’t afford to pay the cost of the low-probability error, so now I ski more safely.

Most of you probably don’t do things quite as stupid as skiing along the edge of a cliff. But then again, I was blind to how my actions were putting me at risk. I’d grown overly accustomed to the dangers of backcountry skiing, and, in turn, I’d grown overconfident. And that brings us to driving…

Driving

When you’re driving, you’re always making lots of little choices, but I’ll oversimply it and frame driving as a choice between two options: Being cautious or speeding and tailgating.

If you choose to drive cautiously, your trips will take a bit longer, and you’ll spend a bit more of your life in a car – a small cost. And most of the time, paying this cost will be an “error” in the sense that you probably wouldn’t have gotten in an accident if you’d driven a bit more recklessly.

On the other hand, if you choose to drive fast and tailgate, you’ll save yourself a few minutes here and there – a small benefit. But once in a while, people who drive like this are “wrong” in the sense that they get into avoidable crashes – crashes with a very high cost for all involved.

So if you go slower, you’ll probably lose a few minutes, but if you go fast, you might lose decades.

For many people, driving is just like skiing used to be for me: Nothing bad has ever happened to you, so it doesn’t feel dangerous. But, if you really think about it – or if you’re unlucky enough to have a bad crash – it becomes quite clear that driving is very dangerous.

On the freeway, we zip around at 60 or 70 miles an hour, in little boxes made of metal and glass, sometimes mere feet away from each other. If you tailgate and give yourself only one or two seconds of following distance, it means that if you’re distracted for just one or two seconds when one of the drivers in front of you makes a sudden change, you’re going to get in a serious accident. Can you honestly say that you’re never distracted for a second or two while driving? Can you afford to be wrong?

Such accidents are, of course, rare for individual drivers, but they do happen. A lot. 36,560 Americans died in car accidents in 2018.⁴ If no one drove excessively fast and no one tailgated, that number would surely be lower.

Career Development

If you’ve got a career that you like and that pays well, it’s easy to settle in and just do your work. But the option of professional development is always on the table. You could self-educate, hone your skills, and expand your knowledge. Or you could choose not to earn more career capital and, instead, simply enjoy more free time.

If you choose to pay the steady, low-cost of professional development via mastering your craft and relentless learning, you might never truly need to have done so. Your career might prove to be stable and reliable for the rest of your working life. Then, in a sense, you’ve made an error.

But it’s also possible that you’ll face some kind of career upheaval. Your job could be automated or replaced by low-wage workers in another country. Or, like that of a type-writer repair-man, your job could simply disappear. If that happens, you’ll need to draw upon the career capital you’ve accumulated over the years. If you’ve just been resting on your laurels, you could be in a lot of trouble.

There’s no easy answer here, but it’s worth asking yourself, “Can I afford to not have a backup plan?”

Buying Health Insurance

Let’s imagine you’re one of the millions of Americans who does not have employer- or government-provided health insurance, so you’re considering buying your own. First, you’ve got to choose whether or not to buy it in the first place. And then, if you choose to buy it, you have to choose between high- and low-deductible plans.

Most years, you don’t get injured or sick enough to require medical treatment, so most of the time, you don’t need insurance. If you buy it and don’t need it, then you’ve paid a few thousand dollars in premiums for nothing – a fairly significant cost for being wrong. But if you don’t buy it, and you do need it, you might be out tens or even hundreds of thousands of dollars in medical bills – a very significant cost. Either way, it’s a gamble.

Most people who can afford to buy insurance consider the costs of those two errors, and choose to buy insurance. But then they’re faced with another, arguably more difficult choice: to buy a high-deductible plan with a low monthly premium or to buy a low-deductible plan with a high monthly premium. (If you’ve never had to make this choice, consider yourself quite lucky.) You wonder, “How much medical care might I need this year?” If you think you’ll need a lot, you buy an expensive plan with a low deductible. If you think you won’t need much, you buy a cheap plan with a high deductible. Again, you’re gambling.

Now, I’ve oversimplified this a great deal, and I know from just my own experience shopping for health insurance that these choices are very complicated and difficult to make. All I want to offer here is a suggestion that part of your thinking process should include applying the principle two errors. At each of the two crossroads I’ve just laid out, there are two possible errors. Before you decide, ask yourself, “Can I afford to be wrong?”

Social Distancing Mandates

In recent weeks, we’ve watched governments struggle with a very difficult decision: whether or not to mandate social distancing in order to combat the coronavirus pandemic.

The cost of shutting down events, social gatherings, and businesses is enormous, so most of our leaders hesitated. They were afraid to commit the error of shutting down our economy too early.

But the other error – mandating social distancing too late – will likely prove to have an even higher cost. If we have failed to slow the spread of coronavirus enough, our hospitals will soon be overwhelmed, and many will needlessly die.

Because the costs of both errors were very high, the decision was very difficult. Unfortunately, that meant the ultimately correct decision was delayed. Had we made the call to implement social distancing earlier, we would have probably done a better job mitigating the pandemic.

And we, as individuals, are all facing our own little versions of this decision. I would like to visit my parents. It would be nice to see them, have dinner, catch up in person, and play some board games. They live nearby, so it would be easy. But they’re also in their 60’s, so they’re at high-risk for COVID-19. I’m probably not carrying the coronavirus, but there is a very real possibility that I am. I could just be carrying it asymptomatically, or I could be in an incubation period and about to get sick. Better not to risk it.

Being Okay With Being Wrong

Making a good decision doesn’t mean being right. Making a good decision means choosing the option where you’ll be okay with being wrong.

Sometimes being wrong means being unnecessarily cautious. Sometimes being wrong means facing the consequences of not being cautious enough. But as long as you’ve carefully considered the two errors and chosen which one you’re okay with, you’ve made a good decision.

It’s difficult to think this way because we want to be right, so we normally frame our decisions around the question of, “What’s the right choice?” But there’s no way to guarantee that we’ll get things right all of the time. So we need to remain open to the possibility of being wrong and ask ourselves, “Which version of being wrong can I tolerate?”

The principle of two errors asks us to consider the consequences of the various ways we can be wrong, and often, it suggests that we choose the likelihood of being a little wrong over the unlikely possibility of a catastrophic mistake.

¹ Gilbert, Daniel. Stumbling on Happiness. Vintage, 2007.

² Kahneman, Daniel. Thinking, Fast and Slow. Farrar, Straus and Giroux, 2013.

³ Taleb, Nassim. The Black Swan: The Impact of the Highly Improbable. Random House Trade Paperbacks, 2010.

⁴ https://www.iihs.org/topics/fatality-statistics/detail/yearly-snapshot