Watch Out for False Negatives

How use of this Statistics Tool can lead to virtue

We love to label things as “good” or “bad”.

Whether it’s with situations, decisions, or people, we tend to exercise such judgment across every domain. e.g. A politician’s agenda, the play-calling of a sports coach, a family member’s big life decision, the quality of that new restaurant, etc.

Sometimes we get it “right”, and our label neatly corresponds to reality, or the way things actually are.* The thing that we identified as “good” is indeed good, and the thing that we categorized as “bad” is, in fact, bad.

When we get it wrong, there are two possible mistakes:

1. We labeled the bad thing, “good”.

2. We labeled the good thing, “bad”.

Depending on how you frame the problem, statisticians would typically refer to the former as a Type I error, or false positive, and the latter a Type II error, or false negative.**

Those who choose to pursue unconditional love of truth presumably aim to live their lives in a way that seeks to minimize the rate of such misclassifications. i.e. If a person were to achieve perfect wisdom and integrity, then his or her judgment would ultimately be free from both false positives and false negatives.

For those of us who have yet to attain such wisdom. . . we are left with 3 options to help us get closer to that ideal:

1. Embrace a narcissistic “This is true simply because I say it is” mindset, content with being wise in our own eyes 😎 and forsaking relation to something greater than ourselves.

2. Bias ourselves towards committing more false negatives relative to today (increase skepticism and label more things as “bad”).

3. Bias ourselves towards committing more false positives relative to today (increase trust and label more things as “good”).

Option 1 (where you simply don’t care at all what anyone else thinks, and you live life primarily to amuse yourself) is certainly a path that can feel good in the short term. But at some point, a face-to-face encounter with Beauty will lead one to realize how ugly and relationship-alienating such an approach can be.

Options 2 and 3 may seem strange at first glance — why do I have to choose between increasing the likelihood of making Mistake A vs mistaking Mistake B? How about making no mistake?

Well, if mistakes were easy to avoid, no one would be making them. . . The difficulty lies in that we are often faced with ambiguous situations where we don’t have access to all of the facts (especially when it comes to making inference on things like what some other person is thinking).

In such situations, we go through our analysis and ultimately make a bet / go with our “best guess” on what the right thing to do is. Our average “best guess” (across all judgments) will be biased either towards being a false negative or a false positive. It’s incredibly unlikely that we would have generated an equal number of false positives and false negatives in our life.

We tend to either be over-critical or over-lenient, overly judgmental or overly accepting, a bit too paranoid or a bit too naive, but rarely do we strike a perfect balance in discernment.

Sometimes an example can better illustrate the concept. Consider the decision of hiring someone for a project. You aim to identify a “good” candidate from the “bad” ones and hope that whomever you hire, does in reality end up being good. How can you know, ex ante, whether you are making the right decision (or the right classification)?

The answer: you can’t. You can only decide which kind of bias you prefer, or which kind of mistake you’re more comfortable making.

“Would I rather make the mistake of hiring a toxic employee or the mistake of turning down an employee who would have been a game-changing all-star?” is the question sitting at the heart of this scenario. Hiring the bad employee would be an example of experiencing a false positive, and failing to hire the good employee would be a false negative.

So, on average, which is worse - a false positive or a false negative? A more conservative disposition would seem to suggest that hiring the wrong employee is scarier. A liberal disposition may say that the risk of getting “messy” is worth not missing out on some innovative leap forward.

They may also be a natural progression to these bias tendencies, where we understand the consequences of false positives early on, and subsequently develop a sophistication for understanding the impact of false negatives. Below is how I’ve seen it play out anecdotally.

In order to survive and increase the chances of living a long life, we appear incentivized to avoid false positives (and hence, accept more false negatives). This is effectively a decision to place our bets on Option 2.

What does that look like? It’s being cautious with whom you select as close friends, which dangerous activities you participate in, how you spend your money, etc.
Fundamentally it’s about not being deceived and not taking excessive risk. The benefit is that you’ll avoid a lot of “bad” things that ensnare others; the downside is that you may be turning down some important “good” things in the process.

You can see the mindset of minimizing false positives at work in various children’s stories. Consider the Little Red Riding Hood or Hansel and Gretel. One of the lessons here is that things aren’t always how they appear (the wolf-looking “grandmother” and the “nice” lady with treats). Something may present itself as “good”, when in reality it’s bad. i.e. The message: “Watch out for the false positive!”

This kind of lesson appears fundamental to establishing a base foundation for success. For example, the local teenagers may be doing drugs, but the teen who recognizes such behavior as a “false positive”, which others have misclassified, can avoid getting unexpectedly derailed from a mission-driven life of virtue and love (or true happiness, if you prefer).

Option 2 can be generalized for avoiding any vice, which, through the mechanism of temptation, will necessarily present itself as a “good”, when it, in reality, involves a bad decision that can lead to destruction.

So, to watch out for the false positive is to build discipline and learn to say “No” when others are saying “Yes”. It’s the spirit of a contrarian.

Option 2 also includes mottos like:

• “Trust but verify”

• “When in doubt, don’t.”

• “Fool me once, shame on you. Fool me twice, shame on me.” (actually, being fooled only once might merit a “shame on me” for the hardcore Option 2 enthusiast)

I think, to some extent, the most “responsible”, industrious, and conscientious personalities would learn towards Option 2, given the more obvious dangers that it protects them from. However, these same individuals might be missing out on some of the power behind Option 3.

The downside of excessive reliance Option 2 is that it creates the disposition of a hard heart. To exclusively implement this option is to increase distrust of others, to over-estimate the likelihood of bad things happening, and to elevate skepticism to a soul-damaging level.

It can be very difficult to persuade someone who loves Option 2 to consider using Option 3 from time to time. Why is that the case?

1. The consequences of a false positive (the mistake of labeling the bad thing “good”) tend to be more concrete. If I open my doors to a thief, he can steal my belongings. If I walk alone in a dark alley, I may be the recipient of a violent attack. If I label sugar and trans fats as “good”, then I may get early heart disease.

   1. The consequences of a false negative, such as judging someone rashly, tend to involve more intangible impacts, such as a loss of a relationship or an opportunity for “meaningful connection” (I use these quotes to emphasize that this is harder to describe than the tangible outcome of bodily or property damage).

2. The consequences associated with false positives are based on commission rather than omission. It’s easier to identify the failure in doing something, but it’s harder to identify the failure in not doing something, since the latter involves an imaginative estimation of “What could have happened, if I had given it a try?”

   1. False negatives (e.g. saying “no” to something, when you would have received more value if you had said “yes” instead) are easier to rationalize away, since the opportunity that was being forsaken can’t be measured. Yet when we experience the consequence of a false positive, it can leave us with a burn that cannot be easily dismissed nor soon forgotten.

3. Pain hurts more than pleasure feels good. We tend to prefer avoiding losses over chasing gains. Basically any of the common behavioral science biases, which are rooted in survival and self-preservation, reinforce the Option 2 mindset.

   1. Choosing Option 3 means potentially experiencing exhilarating highs, but also opening yourself up to getting hit with debilitating lows. If you’ve had a past experience with significant trauma, the idea of encountering suffering like that again sounds incredibly terrible, hence why you might find yourself leaning towards Option 2.

These are the primary reasons I think Option 2 is initially more appealing, and it’s persuasive appeal lies in fear of death and suffering.

However, life is about more than maximizing lifespan (or avoiding pain). A focus on quantity can only take you so far; quality is what reigns supreme. To borrow a quote from Richard Branson:

“The brave may not live forever – But the cautious do not live at all.”

Pursuing Option 3 trains you in the virtue of Courage. It’s putting yourself in a vulnerable position, where you could get hurt. Why do that?

Like the management of the COVID pandemic (and the Branson quote), it comes down to saving lives vs. saving livelihood.

From a material standpoint, taking risks and pursuing something innovative can lead to a level of wealth and worldly success far greater than what the “playing it safe” strategy could produce. Through the lens of the false negative / false positive framework, this entails deciding to pursue an idea (i.e. labeling it as “good”) even if ends up being a failure (a false positive).

Perhaps the greatest benefits of Option 3, however, are not material at all, but rather spiritual and psychological. It’s the risk-taking strategy that makes Love possible, after all (“better to have loved and lost than not loved at all…”).

The core component of Option 3 seems to be trust. I’m currently in a quotes kind of mood, so consider the driving ethos behind these sentiments:

• “You may be deceived if you trust too much, but you will live in torment if you don't trust enough.” — Frank Crane

• “Trust is the glue of life. It's the most essential ingredient in effective communication. It's the foundational principle that holds all relationships.”
  — Stephen Covey

• “He who does not trust enough, will not be trusted.” — Lao Tzu

While trusting the wrong person (i.e. labeling the bad thing “good”, false positive) can cause acute damage, consistently failing to trust the right person (labeling the good thing “bad”, false negative) can rob you of meaningful relationships and opportunities to grow in empathy in the long run.

Option 3 is also found in many spiritual lessons, particularly those found in Christianity. Some examples include appeals to the docility of children, the blind trust of sheep, and the parable of the Good Samaritan (or any story of helping the poor).

With regards to the children, I’m referring to Jesus’ admonition for his followers to become like children and humble themselves. Jesus also frequently describes his followers as sheep, perhaps most notably in the parable of the Good Shepherd. And thirdly, we see Option 3 (avoiding false negatives and embracing the risk of a false positive) play out in powerful moral stories like the parable of the Good Samaritan. I want to spend an extra moment looking at this last one:

• A man was beat up and left for dead on the side of the road. People (including “holy” ones like a priest) kept passing this man by, avoiding him by walking on the other side of the road.

• You can imagine the practicality (and fear) of Option 2 working in the minds of the passersby.

  • “What if this dirty, broken man is up to something nefarious, trying to trap me?”

  • “What if this guy has some kind of disease that can infect me?”

  • “Sure I could help, but I have other people who need me back home, and if something happens to me, I would be letting them down. This stranger is not worth it.”

  • I.e. “While this may be an opportunity to do something good, I’m scared that it might be a false positive. . . that this situation will be ‘bad’ for me. So my choice is to label this as ‘bad’ for me even though it’s possible that it might be good. Right now I’m willing to risk committing a false negative over committing a false positive.”

• What happens in the rest of the parable? The Samaritan (essentially someone from a tribe different than that of the wounded man, who could be considered an enemy, as far as the default cultural mindsets and stereotypes of that day) stopped by with compassion to help this man and be his neighbor.

  • Perhaps more than the others, the Samaritan had reasons for having fear and finding excuses to jump to Option 2, but instead he chose Option 3, which is to embrace the risk of the false positive, and turn away from the proclivity to commit a false negative (e.g. judging this guy and deciding that he is “bad” / not worth the time or risk to help, when actually he was an innocent person in need of support).

I know it may seem unusual to think about lessons of compassion and kindheartedness in terms of opening yourself to experiencing more Type I errors (false positives), but for me this framing actually provides a novel way to illuminate blindspots in my own character.

How often do we consider a desire for control, safety, and risk aversion to be primary limiting factors to kindness and charity?

I encourage you to notice this pattern next time you read something inspirational that leads you feeling more desire for solidarity. Which tendency (accepting the risk of false positives vs false negatives) is the piece of wisdom implicitly encouraging you to pursue?

As a final note, I want to reiterate that pursuing Option 3 exclusively would also be a mistake. The virtues of Prudence and Temperance are built on the muscle memory of Option 2. In fact, we might say that a good base of Option 2 is a prerequisite for truly unlocking the mystery of Option 3; we need a well-formed will and habit of self-control in order to truly own our more aspirational decisions.

What I mean is that there seems to be a natural progression to these mindsets. In the words of Thomas Jefferson (the last quote for this piece 🙂),

“The natural cause of the human mind is certainly from credulity to skepticism.”

Another way of saying this is that we all start with an innocently naive mindset, until we get burned a few times. Then we become doubtful and guarded, approaching life with a little more caution (Option 2). We go from readily believing things (freely assigning the label “good”) to readily doubting things (limiting our label of “good” and liberally judging with the category of “bad”).

There is a certain wisdom that is unlocked from this movement, to be sure. but I think the greatest wisdom is what comes beyond this level.

Do we call it mysticism? A form of intuitive knowledge that transcends any descriptive explanation? Being “fully human”?***

Whatever we would call it, I think the way to access more of it, on average, is by watching out for the false negatives while being less fearful of the false positives.

So then, my fellow truth-seekers, let us pursue the optimal balance of using Option 2 vs Option 3 today, my guess being that we’ll need to spend more time on the latter.

* For the purpose of what I wanted to focus on here, let’s temporarily set aside any arguments around Relativism or the difference between preference claims and objective value. Let’s assume that, given an agreed upon set of priors and first principles, there is an objective ranking of any life outcome/feature such that one can be said to be truly better than another, even if we may not be able to subjectively know or perceive the true status of any particular observation with certainty.

** I’m linking the word “positive” here with judgments where we apply the label “good”. You could, however, treat these in the opposite way, whereby a “positive” measurement, just means the presence of something (as opposed to nothing), which could be either good or bad. For example, in medicine, a false positive could be a test that says the patient has cancer (“bad”) when in fact the patient does not have it (good). For the sake of a colloquial reading, I’m defining “false positive” something that looks “positive” or “good”, but that is in reality, bad.

*** I think we could also reframe this psychological movement as: “Everyone is innocent” → “Everyone is guilty” → “Innocent until proven guilty”