On Tragedy Math
The Strange Arithmetic of Compassion
You can listen to the audio for this post by downloading the Substack app.
“I am deeply moved if I see one man suffering and would risk my life for him. Then I talk impersonally about the possible pulverization of our big cities, with a hundred million dead. I am unable to multiply one man’s suffering by a hundred million.”
-Albert Szent-Gyorgi
On January 29 of this year, 67 people perished in a tragic plane crash caused by a collision with an army helicopter. Just 45 hours later, a Medevac plane crashed, killing all 6 people aboard.
Some simple arithmetic predicts that I should feel 11 times worse about the first accident compared to the second. Yet, they felt more or less similar in how devastating they were. If anything, the second might have felt a little more tragic because the incident involved a young girl and her mother, and the girl had just been released after five months of medical treatment for a life-threatening illness.
How can the gut punch of 6 deaths feel the same as, if not worse than, 67? The answer lies in a peculiar bias in moral judgment, called proportion dominance: we tend to compare proportions rather than raw numbers. Although the tally in the first case was so much greater, the percentage of lives lost were identical. In both crashes, 100% of those aboard died.
This bias leads to interesting decisions such that people are willing to sacrifice 2 lives to save 8 out of 10 total lives at risk, but not when there are 40 total lives at risk. Research in this area finds again and again that people’s willingness to help decreases as the number of victims grows.1 Similar work finds that people judge suffering as less severe when it is shared by others.
This cognitive quirk partially explains our gut-reactions to the well-known thought experiment by Peter Singer:
On your way to work, you pass a small pond. Children sometimes play in the pond, which is only about knee-deep. The weather’s cool, though, and it’s early, so you are surprised to see a child splashing about in the pond.
As you get closer, you see that it is a very young child, just a toddler, who is flailing about, unable to stay upright or walk out of the pond. You look for the parents or babysitter, but there is no one else around. The child is unable to keep her head above the water for more than a few seconds at a time. If you don’t wade in and pull her out, she seems likely to drown.
Wading in is easy and safe, but you will ruin the new shoes you bought only a few days ago, and get your suit wet and muddy. By the time you hand the child over to someone responsible for her, and change your clothes, you’ll be late for work. What should you do?
If you are like most people, you might feel that even considering the financial costs of saving the child seems appalling. Most people feel viscerally that they ought to jump into the water without hesitation, no matter how expensive the suit, the shoes, or the cost of running late for work. However, Singer’s takeaway is that, if we feel the sense of total urgency in this case, we should feel the same way when asked to sacrifice an equivalent amount of money by donating to the millions of children who are dying from famine and disease abroad.
This is hard for people to commit to for a number of reasons. Our motivation to help victims depends partly on our perceptions about how helpful our actions will be. If we have the sense that our dollar is being divided among thousands of victims, our efforts may seem like a drop in the bucket. This is a large driver of the identifiable victim effect, wherein victims with a face and a story evoke more sympathy than victims that are merely statistical. The death of one man is a tragedy, the death of millions is a statistic, so it goes.
The issue becomes even more complex when uncertainty enters the equation. Consider a modified version of the drowning child scenario where, instead of the child being right in front of you, they are thousands of miles away in a different country. Fortunately, there is a witness nearby. Unfortunately, they are incredibly transactional and so you must transfer money to the witness to motivate them to act. This introduces uncertainty when evaluating whether your money will actually be used for good. The witness could just keep it for themselves, or they may use it in another way that you hadn’t intended. Not to mention that we can’t confirm that the child actually exists and is indeed in trouble. In the original scenario, we feel 100% sure that we can save the child. In the second, this percentage is to some extent reduced.
Now imagine that, on a particularly unlucky day, instead of one child, there are 50 children drowning in 50 different ponds, each with one transactional witness. You can donate to one of the witnesses at one of the ponds, or you can split that money among all 50 witnesses, hoping that it’ll be enough to get all of them to act. You are now fairly pessimistic that your money will be enough to motivate all of them, but it is a dreaded decision indeed to choose just one child, or a handful of children, to save. This effectively multiples our uncertainty by 50.
Finally, imagine that there are actually no children in trouble, but the 50 ponds are located near a primary school. Statistically, we can almost guarantee that there will a drowning incident at some time in the future. However, you can donate to prevent this risk by building fences around the lakes so that small children cannot access it. You now have to contend with the fact that there is a chance your money will prevent no deaths at all, whether it be because your money went to build a fence around the wrong pond, or because no future children will ever accidentally wander into one of the ponds.
By the time we reach this level of uncertainty, potential donors throw up their hands and move on. This is perhaps why it is so hard to get people to invest in long-term concerns like climate change mitigation, pandemic preparedness, and AI safety.
My point here isn’t that human’s empathetic capacities are broken, it is that they are limited. Given that there is a ceiling to what humans can intuitively comprehend, we have to think in proportions. Everything terrible in the world could always be made worse. If human empathy relied instead only on raw numbers, we would all still be recovering from PTSD after learning about the bubonic plague in high school. Similarly, when confronted with the fact that millions of children are dying of malaria overseas, potential donors may feel too desolate to act. Conversely, the vastness of these problems justify feeling next to nothing for one small child drowning in a pond.
Therefore, it may be a good thing to be confined to our limited proportional scale of 1 – 100. It makes it possible for us to feel for the 73-out-of-73 people lost in the January plane crashes just as much as the 1-of-1 child drowning in a pond. And we care about that child quite a bit. It is this shortcut that can motivate us to act in cases where we feel we can make a difference, which is perhaps better than any alternative given the hardware we are working with. Our capacity for compassion is limited, but we are doing our best with what we got.
Social
Bluesky: @ryan-bruno.bsky.social
see Baron, 1997; Butts et al., 2019; Fetherstonhaugh, Schelling, 1968, Slovic, Johnson, & Friedrich, 1997