2025-12-28 10:08:19
Correlations provide a very useful, quick way to summarize the relationship between two things (as a single number between -1 and 1). For instance, if we find that self-reported anxiety and self-reported depression have a high correlation (which they, in fact, do), then this suggests a substantial link between the two conditions.
But something odd happens when we calculate correlations involving rare traits: the correlation usually has a small magnitude (i.e., is close to zero)!
To illustrate this, let’s imagine we have some rare trait, Y, which you either have (Y=1) or you don’t have (Y=0). It could be, for instance, whether or not someone has a rare disease (1 means they have it, 0 means they don’t).
Furthermore, let’s suppose a discovery is made that there’s an important link between that disease and a numerical trait, which we’ll call X. X could be, for instance, the percentile a person gets on a certain blood test that relates to the disease. So let’s suppose that X can take on integer values from 0 to 100. Moreover, imagine that it’s discovered that X ALWAYS equals 100 when a person has the disease, but when the person doesn’t have the disease, X can take on any value from 0 to 100 (uniformly at random). In this setup, it seems like X and Y should be strongly correlated – after all, X is always 100 for people who have the disease, and very rarely 100 for people who don’t. But do we find a substantial correlation between X and Y in this case? Well, it depends on the rarity of the disease. So let’s examine the correlation between X and Y (via simulation) as we vary the disease’s rarity from 1 in 2 (a probability of 0.50 of having the disease) all the way down to about 1 in 32,000:
As we can see in the table and chart, when Y is not rare (i.e., 1 occurs with reasonably high probability), then the correlations between X and Y are high. For instance, if the trait occurs in 1 in 2 people, then the correlation between X and Y is r=0.77. But as the trait gets rarer, this correlation drops, until we get to a rarity of about 1 in about 32,000, at which point the correlation between X and Y is minuscule, at r<0.01.
Situations like this can pose a big problem in research using correlations. If we are studying rare traits, we may use correlations to examine what they are associated with. But, as in the example above, using correlations can make rare traits look like they aren’t really meaningfully linked, even to other traits they’re highly related to!
But is the problem I described really a general problem of rare traits, or does it only apply in specific instances, such as the one we simulated above?
Well, first it’s worth noting that it’s POSSIBLE for even an extremely rare trait to have a strong correlation with a separate variable. For instance, if we modify the example above so that, as before, when Y=1 we have X=100, but unlike before, when Y=0 we have X be 0, then we always get a correlation of 1 regardless of how rare it is for Y to be 1. This case is easily explained because here, X and Y perfectly mirror each other, with X simply being 100 times Y.
Let’s consider another example. Suppose that, as before, X=100 whenever Y=1, but now let’s make it so that when Y=0, X has a 50/50 chance of being either 0 or 1. In that case, we get a correlation (r) between X and Y of almost 1 if Y has a 1 in 2 chance of being 1, and a correlation of r=0.41 when Y has only a 1 in 131072 chance of being 1.
We therefore see that this is not a universal phenomenon – it’s possible for a variable to have a high correlation with a rare trait, even though rare traits have a tendency to create low correlations.
What can we say about when these low correlations with rare traits will occur?
We’re going to look at this from two perspectives.
First, let’s consider the special case where X, like Y, is also a binary variable (i.e., it only takes on the values 0 and 1). Furthermore, in this setup, let’s suppose that X is guaranteed to always give half 0’s and half 1’s. For instance, it could be that X represents sex assigned at birth (X=1 corresponds to female, and X=0 corresponds to male, with each occurring about half the time) and Y is whether a blood test came out positive for a disease that only females can get (Y=1 for a positive test result, Y=0 for a negative result).
In this setup, what can we say about the correlation between X and Y, and how does this vary with the rarity of Y=1 occurring? Well, it turns out that the size of the correlation between X and Y in this setup is strictly bounded based on how often Y takes on the value 1 (let’s refer to the probability that Y takes on the value 1 using the symbol “p”). Then, we have this upper bound on the correlation, r, that I derived:
In other words, if X is forced to take on 1 half the time and 0 half the time, the rarer it is that Y takes on 1, the tighter the restriction on their correlation. In that situation, if Y takes on 1 only rarely, then they can’t have a big correlation. Here is a plot of what this upper bound looks like as p varies, showing the maximum possible correlation for each such p:
Why does the rarity of Y=1 place an upper bound on the correlation in this situation? I think it’s because Y is almost always equal to 0 (due to 1 being rare), but since X is restricted to take on the value 0 only 1/2 of the time, that means it has to give a 1 on close to half of Y’s, meaning that it can’t match Y all that often. The less rare that Y=1 is, the less this is a problem.
What about more general cases, though, where Y is still binary but X is a numerical variable that’s unrestricted (unlike the setup above)?
Well, for this, we have a different upper bound on the correlation that I derived. It is only guaranteed to hold when p is sufficiently small (relative to the other terms) – it may be violated if p isn’t small enough. But under those conditions, we have this upper bound on the correlation:
The variables in this equation are two conditional means: the mean value of X that occurs when Y=1, and the mean value of X that occurs when Y=0. There is also a conditional standard deviation: the standard deviation of X when Y=0 (i.e., how much X varies when Y takes on its more common result, which is 0).
If we treat the conditional means and conditional standard deviation of X as fixed, and consider what happens then as p (the probability of Y being 1) shrinks, then we see that this upper bound on the correlation (which, recall, only applies for p small enough) applies a multiplicative factor of sqrt(p(1-p)). That factor sqrt(p(1-p)) is always less than 1, and it approaches 0 as p approaches 0, effectively putting a cap on the size of the correlation. Here’s a chart of the multiplicative effect that sqrt( p (1-p)) has on the equation, forcing a lower correlation as p shrinks:
This bound won’t always be informative, because it’s possible for the first factor to be so big that the whole equation gives an upper bound greater than 1, which means there is no restriction on the correlation. But when the first factor is moderate in size, and p is small enough, this really does enforce a bound on how big the correlation between X and Y can be based on how rare it is that Y takes on the value 1.
Putting this all together: while rare traits aren’t guaranteed to have low correlations to other variables, they often will be forced to have low correlations to other variables merely as a consequence of being rare traits! And the rarer the trait is, the smaller those correlations with other variables will typically be.
But what should you do when this happens? Well, one simple approach is to switch from measuring correlation to calculating Cohen’s d instead. It gives you the “effect size” of the binary variable Y on your other variable X – in other words, it calculates how much bigger X is, on average, when Y=1, compared to how big X is, on average, when Y=0, measured in units of standard deviations. This removes the effect of rarity – with Cohen’s d, it doesn’t matter how often Y takes on 1 vs. 0. Here’s the formula for it, where s is the “pooled standard deviation”:
But could a problem similar to the one we’re describing happen for variables Y that are not binary? So far, we’ve only thought about “rarity” in terms of a binary variable Y, where the value 1 occurs rarely. But there are other ways that a variable could be similar but non-binary. For instance, suppose that Y is a continuous numerical variable, but that it almost always takes on the value 0, with a small probability it can also take on other values in the range 1 to 100. An example of this kind of variable might be responses to a question like “How many days during the past 30 days did you drive a motorcycle that you own?” The vast majority of respondents will respond with 0, whereas a small fraction will give responses in the tens, twenties, or even say 30 if they ride every day.
In that case, could we have a similar situation where, because the variable is 0 so often, it behaves like the binary variable Y we’ve been discussing above, and usually ends up with lower correlations to other variables? The answer is: probably yes! And, unfortunately, the Cohen’s d strategy won’t work for that situation, because Cohen’s d, as it’s usually conceived, requires that one of the variables is binary.
What is one to do in that case? Well, in the case where our Y variable is bounded (i.e., it is known it can’t go below some fixed value Y_min and can’t go above some maximum value Y_max), one approach is to use this “Cohen’s d” like formula that I derived which, unlike normal Cohen’s d, can be applied when neither variable is binary. I’ll call it the “Generalized Cohen’s d.” It’s given by:
Here, sigma_Y is the standard deviation of Y. Additionally, r is simply the regular correlation between X and Y. A neat aspect of this formula is that in the special case where Y is a binary variable, it simply becomes the formula for calculating Cohen’s d using the correlation, r. Here is the standard formula for converting a correlation, r, to a Cohen’s d for a binary variable Y that takes on the value 1 with probability 1/2 and 0 with probability 1/2:
And here’s the more powerful r-to-d conversion formula for a binary variable Y that takes on the value 1 with probability p and the value 0 with probability 1-p:
What do we take away from all of this?
Well, if you’re studying rare traits and what other variables they are linked to, it can be very misleading to use correlations to do so. You may find that the correlations are low even with variables that have a strong link to the rare trait. In that case, you can switch to Cohen’s d, or when the original trait is not binary (but still mostly just takes on one value), you can try the Generalized Cohen’s d that I introduce in this article.
Please let me know if you find any errors in this article – I didn’t have as much time as I would have liked to check all the formulas. I’d also be very interested to know if you have other good ways of handling these sorts of situations.
2025-12-12 04:40:06
A lot of psychological terms don’t mean what people think they mean (at least, not according to psychologists).
There’s an increasing drift between how they get used colloquially in everyday language and the commonly accepted definitions among psychologists. There’s a sense in which the lay usage is “wrong” (in that it doesn’t match more scientific, precise, or technical usage), but of course, language has always been and always will be in flux. At the end of the day, a word does mean what people widely use it to mean. So I think it’s useful to be aware of both definitions for psychological concepts. The everyday concept helps us understand others, whereas the more technical definition is usually more helpful for helping us understand the way the world works. Here’s a list of examples:
1) Gaslighting
Everyday usage: Someone invalidating your perspective or lying to you in order to manipulate you
Precise usage: Manipulation that specifically causes someone to doubt their own senses or their ability to reason
2) Negative reinforcement
Everyday usage: Something bad happens when you do a behavior, so you do it less
Precise usage: Removal of an aversive stimulus after a behavior is engaged in, causing that behavior to increase (not a form of punishment). This is in contact with positive reinforcement, which adds a desirable stimulus after a behavior (which is a different way to get a behavior to increase).
3) OCD
Everyday usage: being a neat freak or someone who needs things done in a specific way
Precise usage: A disorder involving repetitive, intrusive obsessions and/or compulsions (behaviors performed to reduce anxiety) that are time‑consuming or impair function.
4) Depression
Everyday usage: feeling sad a lot
Precise usage: an ongoing near-daily pervasive depressed mood (sadness, emptiness, and/or hopelessness) or loss of interest or pleasure, that coincides with symptoms like fatigue, suicidality, poor concentration, weight change, or feelings of worthlessness.
5) Antisocial
Everyday usage: a desire to avoid being around other people
Precise usage: a personality disorder (ASPD) involving pervasive disregard for or violation of the rights of others, typically involving deceit, manipulativeness, aggression, and a lack of empathy/remorse.
6) Narcissist
Everyday usage: someone who is self-centered or very vain
Precise usage: a personality disorder (NPD) involving a grandiose sense of self-importance and superiority, need for admiration, and reduced empathy.
7) Trauma
Everyday usage: A very upsetting experience
Precise usage: Exposure to someone dying, serious injury, or sexual violence (DSM), or another extremely threatening or horrific event that has a long-lasting negative impact on a person’s mental function.
While there’s a time for going with the flow of culture, and using words however people casually use them, there’s an important role for more technically precise terminology as well. In the cases above, I believe the technical versions of these words are worth knowing about and understanding.
This piece was first written on November 7, 2025, and first appeared on my website on December 11, 2025.
2025-12-12 03:14:22
When you’re predicting how much a variable changes over time using a regression, do you tend to add the baseline value of that variable as a predictor to control for it? If you do, you can end up with misleading results.
For example, if you’re trying to predict change in anxiety in 2025 vs. last year (anxiety in 2025 – anxiety in 2024), you’ll get misleading results if you enter anxiety in 2024 as one of the predictor variables. If this sounds counterintuitive to you, read on. I’m interested in how many researchers might do this and how widely it’s known that this is a problem.
Quite a few papers have found a negative correlation between the signed change in the variable and its baseline value (e.g., see here, here, here, and here). For the reasons we outline below, such results can be expected even if there are no actual changes in x during the study, as long as: (1) the measurements for x1 and x2 are sufficiently noisy, and (2) there isn’t some mechanism whereby higher values of x1 somehow facilitate larger increases (or smaller decreases) in x.
You can grasp the result intuitively by looking at the formula for Δx:
Δx = x2 – x1
The larger x1 happens to be due to noisy measurements, then, as long as the noise associated with measuring x2 is independent of the noise affecting x1, the lower the value of the signed difference, (x2 – x1), will be. And the smaller x1 happens to be, the greater the value of (x2 – x1) will be. In other words, due to regression to the mean, if you take two noisy measurements and calculate the signed difference between them, you can expect that x2 – x1 will be inversely correlated with x1. But in case the intuitive explanation doesn’t work for you, we explain the result in other ways below. We also explain why this result might be a problem.
The Issue:
The issue comes into play for longitudinal studies when the outcome of interest is a signed change in some quantity (e.g., “income in 2020 – income in 2019” or “post-intervention anxiety scores minus pre-intervention anxiety scores”), specifically in situations where you try to control for the baseline value of the same variable (e.g., you include “2019 income” or “pre anxiety scores” as an independent variable in the regression).
We think this problem has implications for how we interpret the results of any papers that predict changes in a variable in this way. We explain the issue in detail below.
Suppose your goal is to study the signed change in some quantity over time. To keep things simple and concrete, let’s suppose you want to know what traits were associated with people becoming more anxious from 2019 to 2020 (on a self-reported anxiety scale). Hence, you might define your primary outcome of interest to be Δanxiety, the signed change in anxiety across time, like this:
Δanxiety = 2020_reported_anxiety – 2019_reported_anxiety
Now, you run a linear regression predicting Δanxiety using various factors to see what is linked to people’s anxiety changing. However, a person’s initial level of anxiety in 2019 (i.e., 2019_reported_anxiety) could be linked to how much their anxiety changes. For instance, if you don’t have a particularly high level or low level of anxiety in 2019, then maybe we should expect it not to change very much, or maybe if you have very extreme 2019 anxiety, we should expect a greater likelihood of it changing. Therefore, in your linear regression, you include as a control (i.e., an additional independent variable) 2019_reported_anxiety.
—
This all sounds very sensible (it’s precisely what we did in a recent study). You may think that controlling for the baseline value is a best practice. The unfortunate thing is that this can seriously bias your results for very subtle reasons!
Before we explain why this is a problem, please consider this puzzle and see what you think the answer is. Note that only 21% of my Twitter followers got this question correct!
—
A test of your math intuition: we use a very noisy but unbiased scale (accurate to +-40 pounds) to measure the weight of 1000 18-yr-old men on Monday and again on Tuesday. By noisy, we mean that each time you use the scale, you can think of it as giving the real weight plus random noise. By unbiased, we mean that on average, the scale gives the right answer (so if you weighed the same person repeatedly hundreds of times and took the average result, it would be very accurate).
Let
Δweight = Tue_weight – Mon_weight
What do you predict for the value of this correlation:
r = Correlation(Mon_weight, Δweight)
Option 1: r ≈ 0.00
Option 2: 0.1 < r < 0.9
Option 3: -0.9 < r < -0.1
Option 4: r ≈ 1.00
—
Answer: once you’ve thought about the question above, here is the answer (turn your phone upside down to read it):
ɹǝʍsuɐ ʇɔǝɹɹoɔ ǝɥʇ sᴉ ǝǝɹɥʇ ɹǝqɯnu uoᴉʇdO
—
Despite the issue we’ve outlined, it seems not uncommon for papers to predict the signed change in a variable using a set of variables that includes the baseline value of that variable. They don’t seem to discuss this problem, either. For example, see here, here, here, and here.
—
Why, if you are predicting a signed change in a variable, is it not okay to include the baseline value of that variable in linear regression?
The issue is that the signed change in a variable (e.g., Δweight = Tue_weight – Mon_weight) and the baseline value of that variable (e.g., Mon_weight) are going to be negatively correlated automatically in the absence of other factors, just as a result of how those two variables are defined (not due to any empirical fact about the world). So including both in a regression not only gives a misleading coefficient (i.e., it may show a negative relationship between them even when empirically one does not exist), but it may cause your whole regression to be misleading (e.g., p-values don’t have the interpretation you expect).
The negative correlation might lead some to conclude, for example, that the higher someone’s anxiety was prior to some intervention, the more their anxiety level dropped after the intervention – yet such a negative correlation (between baseline anxiety and the [anxiety at time point 2 – anxiety at time point 1] value) could arise even if there are no real changes in anxiety from one time point to the next!
—
The intuition here is that this is due to a form of regression to the mean. We usually think of regression to the mean as occurring when you purposely select for some subset of a population (e.g., those who perform best on a test), and then in the next time period, we expect to mean reversion. In this case, though, measurements that, due to chance, happen to be high will tend to fall (due just to regression to the mean), meaning the signed change between the two years will tend to be negative. And measurements at time one that happened to be smaller than normal due to noise will tend to rise the next time period (again due to regression to the mean), meaning the second value minus the first value will tend to be higher. So high time period one values will tend to have negative changes, and low time period one values will tend to have positive change values, leading to a negative correlation between the two of them.
If that’s still not intuitive for you, consider the opposite relationship – the one between the value of a variable at time point 2 and the signed change, calculated as (value at time point 2 – value at time point 1). It is true (and hopefully also intuitive for you) that larger values at time point 2 will be positively correlated with larger improvements from time point 1 to time point 2. (And, similarly, if time point 2 happens to be worse, then (value at time point 2 – value at time point 1) will be negative.)
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What can be done about this?
There seem to be a few ways to resolve this issue.
(i) Instead of predicting the signed change in a variable, predict the final (time point 2) values. Then it’s okay (and often advisable!) to control (i.e., include as an independent variable) the baseline value. The issue discussed above is only a problem if you’re predicting the signed change in a variable, not if you’re predicting the value of the variable at time point two.
(ii) If it’s important to predict the signed change value (for instance, because that’s what you fundamentally care about), then it’s better not to control for the baseline value at all than to control for it and distort your results.
(iii) Several other approaches are summarized in the following paper: Chiolero et al. 2013
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Thanks for reading – we’d love to hear your thoughts about this issue! Please comment below or contact us directly if you have any thoughts.
—
Some time after we wrote this, we later came across some papers talking about this phenomenon. (For an overview and some approaches to responding to it, see: Chiolero et al. 2013: https://www.frontiersin.org/journals/public-health/articles/10.3389/fpubh.2013.00029/full)
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Acknowledgements:
I noticed this phenomenon in a dataset and my colleague Clare hypothesized that this phenomenon was to blame. We then confirmed this together. I wrote most of this post, and she added examples from the literature and the Chiolero et al. paper.
2025-12-07 02:07:56
I believe that if you are healthy and have a healthy diet, then taking 30+ supplements per day (even if you spend a ton of time researching which ones to take) has a net negative expected value on your health.
The two fundamental issues are:
Issue 1: That every supplement has:
-a chance of harmful interactions with other drugs/supplements (and as you take more and more, the number of potential interactions grows quadratically – like supplements squared)
-a chance of contamination (e.g., with lead, or with compounds not mentioned on the label), which is not as rare as one may think
-a chance of negative interactions with your biology (e.g., nearly every studied medication is found to cause some side effects more often than a placebo)
Issue 2: That almost all supplements, when eventually *rigorously* tested on general healthy populations (i.e., they are not populations with a specific disease or going hungry etc.) show no health benefits. So the risks from Issue 1 are unlikely to be compensated for.
Of course, this does not mean that ALL supplements don’t work. For instance, creatine likely helps build muscle mass for those trying to bulk up, most strict vegans should supplement with vitamin D and B12, and people with darker skin living in less sunny climates are at elevated risk for vitamin D deficiency. Omega-3s are likely not harmful and may even give you some benefits. If you test low in an essential vitamin or mineral, that’s, of course, a good reason to supplement it. And there are some impoverished areas of the world where basic nutrition is routinely not met, in which case supplementation with vitamins/minerals can be life-saving. Multi-vitamins from reputable companies that undergo third-party testing are at least very unlikely to harm you much unless they include mega doses. But once you start taking large doses, or compounds your body doesn’t normally encounter, and especially when you start taking many at once, supplementation becomes riskier.
One other caveat: some of the “all in one” kinds of supplements put so little of many of the compounds in the supplement that while, thankfully, they aren’t likely to hurt you, it also pretty much rules out the benefit as well. Dose-response cuts both ways.
Overall: my point is not that all supplements are useless, but about the risk/reward profile of taking *tons* of them at once: that ordinary people end up worse off (unless the dosages are too small to realistically get any benefit).
This piece was first written on December 6, 2025, and first appeared on my website on December 22, 2025.
2025-12-03 03:07:39
I have a number of intrinsic values, but two of my most important intrinsic values are happiness and the lack of suffering for conscious beings. While these are fairly common intrinsic values, I suspect many people actually value them more than they realize. In other words, upon careful reflection, many people would realize that happiness and lack of suffering are stronger intrinsic values to them than they previously were aware of.
With that in mind, here are seven thought experiments related to happiness and suffering that might make you see your intrinsic values a bit differently:
— we don’t necessarily know our values —
Unfortunately, our deepest values are not something we automatically know about ourselves. The conscious side of our mind doesn’t have direct access to the rest of our mind. And much of what we care about lies in the subconscious, meaning that our explicit beliefs about our values may not be comprehensive or even accurate. So this at least opens the possibility that we might subconsciously value increasing strangers’ well-being more than we realize.
— our values are affected by our beliefs —
Some of what we value hinges on our beliefs about what’s true. And so if some of our relevant beliefs are false, or we haven’t fully explored all the implications of those beliefs (e.g., two things we believe imply a third thing but we haven’t realized that), then what we think we value may be, in a certain sense, “wrong”. So this at least opens the possibility that we might hold beliefs that are false or that contradict each other, such that, once they are corrected or the contradictions are resolved, we may end up caring more about increasing the well-being of strangers than we think we do now.
— our understanding of our values evolves —
We figure out our own values over time as we carefully introspect, discuss our values with others, compare options, notice and resolve contradictions, refine our understanding of the truth, flesh out the implications of what we already think is true, and infer things about ourselves from our own reactions. Hence, it is not that strange to think that our understanding of our values may change as we engage in reflection.
— a growing ember of classical utilitarianism —
So we may not fully understand what we value.
And I am proposing that through thought experiments about values, if carefully considered and reflected upon, quite a lot of people may realize that they care more about working to increase happiness or reduce suffering than they had originally thought. That many people are *partly* classical utilitarians in their values, even if they haven’t realized it, and that thought experiments can expose this.
— the thought experiments —
Warning: references to intense suffering and very difficult tradeoffs
(1) Suffering is bad, and not just for me
Remember that time when you felt really intense physical suffering (e.g., maybe you had a really nasty stomach flu)? Don’t dwell on that time, because I don’t want you to suffer now, but remember it just for a moment. Remember how much that suffering sucked?
Now take a few seconds to imagine a stranger. Someone you’ve never met and never will meet, but perhaps you passed them on the street at some point in your life. Take a moment to picture their face.
Now, suppose that right now this stranger is suffering in that same exact way that you recalled yourself suffering a moment ago. Assume this person is not someone who has done something terrible to deserve that suffering.
How do you feel about a state of the world where this stranger is suffering? Contrast it to a state of the world where that person is happy. I bet you think the latter world is better than the former.
I ran a survey asking people about their intrinsic values, that is, those things they value that they would continue to value even if no other consequences occurred as a result of that thing. In it, 49% of people (from the general U.S. mechanical Turk population that seemed to understand the question) reported that “people I don’t know suffer less than they do normally” is an intrinsic value, and 50% reported that “people I don’t know feel happy” is an intrinsic value.
It’s tough to measure people’s intrinsic values, and this is not a population that is fully representative of the U.S. population, so the exact numbers should be taken with a grain of salt. But these results suggest to me that many people do care about the suffering of strangers.
But now, the next question is, what properties should your caring about strangers have?
—
(2) Your friends care about the suffering of their friends
You presumably want the world to contain more of what your friends value (and less of what they disvalue) insofar as these values don’t conflict with your own.
Well, there’s a very good chance that one of the things your friends value is that their friends don’t suffer. Another thing your friends probably value is that their own friends get the things they value too, which presumably includes not wanting the friends of their friends (who are the friends of your friends’ friends) to suffer.
In other words, just by caring about the values of your friends, you may also care about the suffering of a whole host of other strangers. Not necessarily all strangers, but a lot of people you will never meet.
—
(3) More suffering is worse (a.k.a. scope sensitivity)
Suppose that 1 innocent person experiences a painful electric shock for one hour. How bad do you feel that is? Now suppose that, instead of that, 100 innocent people each experience the same electric shock for one hour. How much worse does that seem to you? Take a moment to consider it.
Now 10,000 people. How bad is that? Now 1,000,000 people. How bad is that?
At first, you may feel on a raw gut level that the 1,000,000 suffering is not that much worse than 1 person suffering. But are you really taking into account how many people 1,000,000 is? That’s about the entire population of San Francisco.
Notice how, when you really think about it, and you really try to get the enormity of the large numbers, 1,000,000 innocent people each experiencing a painful electric shock for one hour is way, way, way worse than 1 person experiencing it. Not just, say, twice as bad. But MUCH worse.
That implies that, for instance, eradicating a common and horribly debilitating disease that ten million people would otherwise get is not just a little bit more valuable than helping, say, 1000 people live slightly easier lives. It’s way, way, way more valuable!
I’m not saying you necessarily value a reduction in 1 million units of suffering as being 1 million times more valuable than a reduction in one unit of suffering, just that you probably do think it’s MUCH more valuable.
—
(4) Selfishness does not dominate
What’s the thing you value most in the world? Your life, maybe? Or your happiness? Or maybe something involving another person? My guess is that no matter how much you value this, there is an amount of suffering you’d be willing to give this up to alleviate.
For instance, if you had to give up your life to prevent all future suffering on earth, I bet you would do it, as terrible and unfair a choice as it would be to make.
—
(5) We should help suffering strangers when it is easy (a version of the famous drowning child thought experiment that Peter Singer has popularized)
Suppose a stranger you’re walking behind suddenly teeters and then collapses in front of you. The person is now lying on the ground, clearly in tremendous pain. You are the only person nearby.
I think most of us feel that even though we didn’t cause this person to be ill, we still have a moral obligation to try to help them. That is, (a) not being the cause of suffering doesn’t make us totally off the hook with regard to trying to relieve that suffering.
Furthermore, suppose that it would be a small inconvenience for us to help this person (e.g., we might have to show up 15 minutes late to a fairly important work meeting). I think most of us would still help this person (and would feel that it is the right thing to do). If true, that suggests that (b), if the size of the potential reduction of suffering to another person is much greater than our own loss by our helping them, we probably should help.
Finally, suppose that instead of this being a stranger right in front of us, we imagine that this is a stranger who we happened to have accidentally just Skype called by accident (by entering our friend’s user ID incorrectly). Assuming we don’t believe the person on the other end is faking, shouldn’t we still try to figure out some way to help this person (assuming it is feasible), even though they are far away? Of course, if we have no way to help them, obviously, we have no obligation to help. But suppose we can think of an easy way to help, shouldn’t we do it? This suggests that (c) our obligation to help doesn’t depend on how far away someone is, only on our ability to help that person.
We must then remember, of course, that there are people we could help around the world at little inconvenience to ourselves.
Even if you agree with (a), (b), and (c), that doesn’t mean that you think you should devote all your time and money to helping people who are suffering. But if you do agree with those points, then I suspect your value system tells you that you should expend at least some of your resources helping reduce suffering in others, if you have the means to do so without too much sacrifice.
—
(6) Other values may seem to diminish when happiness is even slightly reduced as a consequence of them
Suppose that you happen to have found out that (through no action on your part) certain people have a false belief about a certain topic. Furthermore, you know they would believe you if you corrected this belief.
The problem is that these people would all be slightly less happy if they knew the truth about this thing, and in fact, nobody would benefit in any way from this truth being known.
Would you tell these people? Well, you may think truth is important (I do too), but you may feel that it substantially takes the wind out of the sails of truth if all people involved are less happy because of it, and nobody benefits. I think in this case, some people will say, “What is the point of the truth if everyone suffers slightly more because of it?” In other words, they might feel the value of truth is reduced to almost nothing.
This isn’t just about truth. For instance, you can do a version of this thought experiment about equality (what if, in a particular group of people, you could make the group more equal in some dimension, but every single member of the group would be slightly less happy as a result). Or you can do it for almost any other value.
My guess is that these other values seem quite a bit less valuable (and perhaps to some not even valuable at all) when everyone is slightly less happy as a consequence, highlighting the potential importance of happiness in your value system.
Note that you may not necessarily feel this property is symmetrical with other values. For instance, suppose that someone reduces suffering a significant amount, but in doing so causes the people involved in the situation to have slightly less accurate beliefs. You may not feel that the slight reduction in accurate beliefs makes the reduction in suffering itself any less valuable.
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(7) We can at least agree on suffering
Some people like apples and others like oranges. Some want to spread atheism, and others want to spread theism. Some people think you should obey authorities, while others value freedom of thought. But one of the few dimensions we are just about all similar on is that we don’t want to suffer ourselves, and we don’t want the people we love to suffer.
Some people are perhaps exceptions (e.g., Christopher Hitchens claimed Mother Teresa believed suffering to be at least sometimes good, quoting her as saying “I think it is very beautiful for the poor to accept their lot, to share it with the passion of Christ. I think the world is being much helped by the suffering of the poor people.”) I’m not sure what she meant by that or whether she would apply that to her own suffering or that of her loved ones, but it’s a possible exception.
That being said, though, disagreement on the badness of suffering seems really rare. Nearly everyone seems to find suffering bad, at least when it happens to themselves or their loved ones.
So if we all had to work as a species to reduce one thing, suffering seems like a pretty good contender. It’s hard to think of another thing we all dislike more.
— final thoughts —
Taken together, these thought experiments suggest (insofar as you buy into them) that you may believe:
(1) Suffering is bad when it happens to strangers
(2) You at least somewhat care about the suffering of many strangers by virtue of caring about the values of those people you care about
(3) More suffering of strangers is worse than less, and way, way more suffering is much worse still
(4) Your own self-interest is not more valuable than the potential for reducing all the suffering in the world
(5) We should put at least a little effort into reducing the suffering of strangers if it’s not too costly for us to do so, and we should not care whether those strangers are far away or near
(6) Most other values don’t seem as great if the result of producing them is to cause everyone involved to suffer slightly more, with no one benefiting, and these other values may even seem to lose their value in these cases
(7) We can all at least agree that suffering is bad and work together to reduce it
These points are not the same as classic utilitarianism, but they point in roughly the same direction as it does, I think. And anecdotally, some people seem to be quite impacted in their ethical views by thought experiments like these (though of course we can’t be sure it’s because they are revealing their deeper values as opposed to actually reshaping those values).
I don’t think that increasing the happiness of and/or reducing the suffering of conscious beings is the ONLY thing you care about. Nor do I think you SHOULD only care about those things.
But perhaps these thought experiments will make you realize that you care more about them than you thought you did, or that you’re more of a classic utilitarian than you realized.
This piece was first written on June 2, 2018, and first appeared on my website on December 2, 2025.
2025-11-19 09:48:22
A lot of psychological terms don’t mean what people think they mean (at least, not according to psychologists).
There’s an increasing drift between how they get used colloquially in everyday language and the commonly accepted definitions among psychologists. There’s a sense in which the lay usage is “wrong” (in that it doesn’t match more scientific, precise, or technical usage), but of course, language has always been and always will be in flux. At the end of the day, a word does mean what people widely use it to mean. So I think it’s useful to be aware of both definitions for psychological concepts. The everyday concept helps us understand others, whereas the more technical definition is usually more helpful for helping us understand the way the world works. Here’s a list of examples:
1) Gaslighting
Everyday usage: Someone invalidating your perspective or lying to you in order to manipulate you
Precise usage: Manipulation that specifically causes someone to doubt their own senses or their ability to reason
2) Negative reinforcement
Everyday usage: Something bad happens when you do a behavior, so you do it less
Precise usage: Removal of an aversive stimulus after a behavior is engaged in, causing that behavior to increase (not a form of punishment). This is in contact with positive reinforcement, which adds a desirable stimulus after a behavior (which is a different way to get a behavior to increase).
3) OCD
Everyday usage: being a neat freak or someone who needs things done in a specific way
Precise usage: A disorder involving repetitive, intrusive obsessions and/or compulsions (behaviors performed to reduce anxiety) that are time‑consuming or impair function
4) Depression
Every day usage: feeling sad a lot
Precise usage: an ongoing near-daily pervasive depressed mood (sadness, emptiness, and/or hopelessness) or loss of interest or pleasure, that coincides with symptoms like fatigue, suicidality, poor concentration, weight change, or feelings of worthlessness.
5) Antisocial
Everyday usage: a desire to avoid being around other people
Precise usage: a personality disorder (ASPD) involving pervasive disregard for or violation of the rights of others, typically involving deceit, manipulativeness, aggression, and a lack of empathy/remorse.
6) Narcissist
Everyday usage: someone who is self-centered or very vain
Precise usage: a personality disorder (NPD) involving a grandiose sense of self-importance and superiority, need for admiration, and reduced empathy.
7) Trauma
Everyday usage: A very upsetting experience
Precise usage: Exposure to someone dying, serious injury, or sexual violence (DSM), or another extremely threatening or horrific event that has a long-lasting negative impact on a person’s mental function
While there’s a time for going with the flow of culture, and using words however people casually use them, there’s an important role for more technically precise terminology as well. In the cases above, I believe the technical versions of these words are worth knowing about and understanding.
This piece was first written on November 7, 2025, and first appeared on my website on November 18, 2025.