We tend to assume people understand certain basics, but maybe they don't
Did you know that more than 99% of the US population is split about evenly across California, Texas, and New York City (meaning that less than 1% of Americans live everywhere else in the country)? Did you know that the US adult population is 41% black, 39% Hispanic, and 29% Asian?
Maybe you were dubious about that first assertion, and if you did the math, then you figured out the second one is not mathematically possible. Nonetheless, these were the estimates given by a sampling of 1,000 US adults in a recent YouGov / Newsweek poll. Here’s a snapshot:
It’s clear from these survey results that intuition fails a lot of people when it comes to their notions of US demographics, but I think it’s possible these results might also speak to something even more fundamental. I think it’s possible that a lot of people are also simply bad at gauging proportions and percentages in general. How well would people do if they were gauging different piles of colored beads or ping pong balls instead of guessing about something as potentially loaded as race, class, and gender demographics? I suspect the results would be better than what came out of this survey, but I bet it would still be shockingly bad. What else other than basic innumeracy explains answers with so many non-overlapping proportions that add up to well over 100 percent?
The Wheat and Chessboard Problem
There are many versions of the problem. In some versions it’s wheat, and in others it’s rice. It’s a folktale about the invention of chess, or about a king losing single game of chess to his servant, or not about chess at all.
But in all versions of the story, the essence is that a king offers one of his subjects a reward for something, and for his reward the man requests that grains of wheat (or rice) be measured out for him on the king’s chessboard, doubling with each square. One grain on the first square, two on the second, four on the third, and so on.
The king, baffled by such a small price, immediately agrees. But then his treasurer informs him that such a reward would outstrip the resources of the entire kingdom and much more.
The simple message of the story is that people don’t understand exponents. Exponents are beyond our natural conception. This has been made very clear during the pandemic, particularly in the discourse around how COVID-19 spreads and how to mitigate spread – a problem that is very clearly about exponential curves. There have even been some studies about how correcting these misperceptions is helpful during a pandemic.
They Blinded Me with Science
In my own engagement with vaccine skeptics, anti-maskers, and COVID-deniers over the last couple of years, I have found that a lot of people don’t know what “per capita” means. I’m bet that some of them are gaslighting or trolling, but a lot of them surely don’t know what it means, and as a result they simply ignore it. I have both participated in and observed mutually-frustrating interactions between people, where Person A insists the vaccine doesn’t work, only to have their evidence crumble when Person B explains that their data shows the opposite if they would actually consider the “per capita” part. But then, as often as not, Person A still fails to grasp the difference.
I’ve been involved in similar conversations where it became clear the other person didn’t understand what it means in a scientific or research context to “control for” variables. I mean, they didn’t have the slightest idea what the phrase means let alone why the concept is important. And I imagine that a lot of people who do understand the concept of controlling for variables have limitations when it comes to the actual math involved. I’ll count myself as part of this group.
Expertise and Lack Thereof
We have relatively reliable ways of judging whether someone has subject matter knowledge germane to the issue at hand. We can know whether we’re dealing with an epidemiologist, a social scientist, etc. Even when we’re talking to random lay people, we gather clues about their level of expertise from the ways they cite sources and evidence, and from the nature of the sources themselves. Sometimes it’s clear that a person’s domain knowledge is lacking. One example of where this jumps out for me is when people talk about what the President or Congress should do about this or that problem, and the person’s notion of what’s possible is completely detached from realities like separation of powers and the Senate filibuster. The key point here is that in cases where we can judge the other person’s domain knowledge, we can make relatively informed calculations about the costs of engaging with them. We have a sense of what they do and don’t understand, and we can meet them at a mutually-beneficial level if we want to. Or at least we can make an informed go at it.
The Black Box
When we’re engaging with other people on an issue, their ability to understand basic fundamental concepts is a black box to us, unlike their level of domain knowledge. I think I naturally assume that most people have a basic grasp of how proportions work, and a grasp of basic concepts like “per capita” and “controlling for” variables. And so when someone disagrees with me, it often feels like they are taking an ideological stance. I assume it’s willful, that they are not willing to consider evidence that challenges their views. However, it’s entirely possible that the main obstacle, the cause of the gulf between us, is not their ideology or even domain knowledge, but gaps in their (or my!) grasp of fundamental concepts.