Americans’ abysmal ability to estimate group sizes

November 8, 2022 • 10:30 am

I found this article fascinating, and the explanations intriguing.  Two YouGov polls surveyed 1,000 Americans (2,000 total) in January of each year, asking people to estimate the proportions of Americans in 43 different groups.  A large number of these estimates were wildly inaccurate, particularly when minority groups were surveyed (estimates were way too high) as well as “majority” groups (e.g., “Christians”), where estimates were too low. Read on; there’s a sociological explanation for such mis-estimation, though I don’t know how well supported it is.

Click to read (it’s free):

First the data, with calculations explained in the figure:

The pattern is one of overestimating the sizes of minority groups and underestimating sizes of majority groups. Groups hovering around the middle tend to be estimated more accurately:

When people’s average perceptions of group sizes are compared to actual population estimates, an intriguing pattern emerges: Americans tend to vastly overestimate the size of minority groups. This holds for sexual minorities, including the proportion of gays and lesbians (estimate: 30%, true: 3%), bisexuals (estimate: 29%, true: 4%), and people who are transgender (estimate: 21%, true: 0.6%).

It also applies to religious minorities, such as Muslim Americans (estimate: 27%, true: 1%) and Jewish Americans (estimate: 30%, true: 2%). And we find the same sorts of overestimates for racial and ethnic minorities, such as Native Americans (estimate: 27%, true: 1%), Asian Americans (estimate: 29%, true: 6%), and Black Americans (estimate: 41%, true: 12%).

A parallel pattern emerges when we look at estimates of majority groups: People tend to underestimate rather than overestimate their size relative to their actual share of the adult population. For instance, we find that people underestimate the proportion of American adults who are Christian (estimate: 58%, true: 70%) and the proportion who have at least a high school degree (estimate: 65%, true: 89%).

The most accurate estimates involved groups whose real proportion fell right around 50%, including the percentage of American adults who are married (estimate: 55%, true: 51%) and have at least one child (estimate: 58%, true: 57%).

This tendency to overestimate small groups and underestimate large ones has been seen in other studies.  The data that fascinate me are of course the wild overestimate of the population of Jews and Muslims (often cited as trying to “take over the country”, as well as of atheists and gays.  I thought everybody had a rough idea of the proportion of blacks in the U.S., but this, too is grossly overestimated. And how people can think that 30% of Americans can live in New York City eludes me (30%, like all the figures, are medians among guesses). If that were true, the city would have a population of 100 million!

On the underestimage size, disparities are smaller, but one of them surprises me: the median estimate of proportion of people who have read a book in the last year is just 50%, while the actual figure is 77%. I’m not sure abut the reason for this disparity, but I’m still horrified that only about 3/4 of Americans have read a book in a whole year (frankly, I would have guessed that it would be less).

The authors note that the overestimates of minority groups aren’t likely to be due to fear of such groups, since actual members of those groups tend to show the same degree of overestimation as do non-members. That, too, baffles me. How could a Jew think that 30% of Americans are Jewish? I always knew it was about 2%, and that’s the correct proportion.

Now, what’s the explanation? Here’s what YouGov says:

Why is demographic math so difficult? One recent meta-study suggests that when people are asked to make an estimation they are uncertain about, such as the size of a population, they tend to rescale their perceptions in a rational manner. When a person’s lived experience suggests an extreme value — such as a small proportion of people who are Jewish or a large proportion of people who are Christian — they often assume, reasonably, that their experiences are biased. In response, they adjust their prior estimate of a group’s size accordingly by shifting it closer to what they perceive to be the mean group size (that is, 50%). This can facilitate misestimation in surveys, such as ours, which don’t require people to make tradeoffs by constraining the sum of group proportions within a certain category to 100%.

This reasoning process — referred to as uncertainty-based rescaling — leads people to systematically overestimate the size of small values and underestimate the size of large values. It also explains why estimates of populations closer to 0% (e.g., LGBT people, Muslims, and Native Americans) and populations closer to 100% (e.g., adults with a high school degree or who own a car) are less accurate than estimates of populations that are closer to 50%, such as the percentage of American adults who are married or have a child.

I suppose this could be called “psychological regression to the mean.” It doesn’t fully convince me, though, because I’d think people would go on their “lived experience” rather than assume their experience has given them a biased sample of the size of a group. But I haven’t read the meta-study in the link.


h/t: Winnie

48 thoughts on “Americans’ abysmal ability to estimate group sizes

  1. I would love to see a chart including group representation in popular media. Around 12% of US citizens are African-American; but people reportedly believed the number was around 40%. It seems like what I see on American television lately has shown the number to be around 30-40% – and it has been consistent in the news, pop culture, etc.

    1. That estimate is probably heavily influenced by the demographics of the inner cities, where Black people are often an actual majority.

  2. I like the ones relating to race the most. Hopefully, those people didn’t have the same responses for each race, because that would be 196% of the population. I also like the people think 30% of the population lives in Texas.

    1. > that would be 196% of the population

      There is a statistical methodology that I believe works better in some contexts: sliders. For each demographic question, have a bar with multiple sliders on it. The area between 0 and the first slider is the white population; the area between the first and second sliders is the African-American population; the area between the second and third is the Asian population, etc. It works for categories with clear-cut definitions (income, education, age, some racial questions).

      The simultaneous advantage AND disadvantage is that it only goes to 100, meaning individuals can only be counted once. People with multiple identity groups in the same category might want to be counted twice – or not at all. “Mixed race” would have to be a separate category on the main bar, and non-racial ethnicities (Italian, ginger, etc.) would not fit on the bar at all.

    2. They also think 32% live in California. I think a very large portion of US citizens are innumerate, so most of the answers they give to these kinds of questions are not based on careful reasoning, but are just random numbers picked out of the air.

  3. The ethnicity estimates are interesting and also could be of concern. Interesting because of all the domains surveyed they are visible so that people have direct experience (knowledge?) of exemplars of the various groups. How could Americans on average think that 40% of the population is Black given their everyday experience (not counting media)? Perhaps of concern because of implications for misperception of discrimination or other societal concerns? If 40% of the population is Black, then how come 40% of X occupation are not Black? And if 40% of the population is Black, then Blacks are not so over-represented in prisons as they actually are.

    1. You did mention media. If we go by TV commercials, nearly everyone in North America is black. And half of them are gay, even the ones with two-parent families. And of course all are wealthy enough to buy whatever is being advertised, which is the main thing.

      TV seems to be getting less diverse, though. While once the ad producers did cast a range of people in group scenes, like customers lined up at a Tim Hortons, the ads featuring mini-dramas of two or three people interacting are now heavily black and the other races have mostly disappeared.


      1. Now most all of the TV villains are white and the victims/heroes are minorities. As are all the cars and pet owners are minorities, too. Payback for when it was the reverse, so I can’t really object. But it’s not your imagination.

  4. I remember similar statistics in the UK some thirty years ago in which people vastly overestimated the percentage of the black/Asian/Muslim population; in most cases it was pretty clear their motivation was a belief that the UK was being “overrun” by these groups.

    However, one note on the “actual” percentages quoted in the graph: atheists only 3%? I’m pretty sure that’s now a wild underestimate, which makes me wonder about some of the other “actual” percentages.

    1. I guess that the word “atheist” has strongly negative connotations to many Americans, so nonbelievers are more likely to describe themselves as “not religious” or “nothing in particular” or “religiously unaffiliated” than out-and-out “atheist.”

    2. I noted exactly that same 3%. The ‘nones’ have grown to well over 20% of the population. Would less than 15% of them be atheist? I would be very surprised there.
      There are other confounding factors, such as the ‘one drop rule’ in the us. Many blacks would be considered coloured (of mixed race) here.
      The late General Colin Powell was considered black in the US, but as Dawkins pointed out, showing a photo of Bush, Powell and Rice, if an alien had to divide these 3 into two groups, it would be Powell and Bush in one, and Rice in the other (not looking at genitals). I can’t find his particular photo, but there are more.
      This one has Rumsfeld too, for good measure, but the point remains, I’d bet that Powell had more white European ancestors than black African ones.

      On an aside, what happened to Condoleeza Rice? She was -despite some minor issues- the embodiment of what a decent Republican should be. (In that sense she also may stand out in that photo).

      1. HBO has a new documentary on the Automat restaurants. There was an interview with an elderly gentleman talking about how he never felt unwelcome at an Automat although he was black. I thought, “is he black?” then noticed that the subtitle identified him as Colin Powell.

    3. I wouldn’t know about 30 year old data in the UK, but your interpretation can’t be generally true because the minority populations themselves overrate their own population the most in such surveys (PCCE says something to that effect, too). Black people in the US or immigrants in Germany tend to concentrate in certain neighborhoods where they are the majority. They extrapolate from what they know. In the US, clearly, opverrepresentations in the media and public life have a huge effect. From Germany and other West European countries, I remember somewhat older data where the minority percentages guessed depended heavily on the composition of the respondents’ own neighborhood. Also, there is an effect of youth bias: In the young generations, recent immigrants or their decendants comprise much higher percentages than in the older generation. The people you see on the streets — schoolchildren, groups of adolescents, mothers with prams, workers — tend to be younger and thus more heavily skewed toward the minority part of the population than the population average.

      1. True, but the smaller the real percentages of these groups are, the less significant are the effects of *their* misunderstanding as a component in the mix, versus that of the white majority. In the UK, the percentages of all these groups were much smaller at the time than in the US (and still are). See the graphs for 1991, 2001, and 2011 respectively here: — thirty years ago the country was nearly 95% “White British”, at a time when people were routinely imagining “Asians” (for which the default meaning in the UK is Indians and Pakistanis) and Afro-Caribbeans as representing 10 to 20% of the population each — an order of magnitude error.

  5. Some incredible discrepancies there – and yes, as DrBrydon says, the idea that 30% of adult Americans live in Texas is noteworthy, to say the least.

    I was surprised by the “true proportion” of atheists given as 3% – maybe I’m showing my own bias but I thought it was higher now?

    1. I wondered about the atheists one. You can find figures that give a higher %. In a 2017 Gallup poll, 12% of Americans said “no” to a question about whether they believe in God.

    2. I think the proportion of people who claim to be “not religious” is higher, but the number of self-identified atheists is probably indeed that low.

      1. Yes, I expect you’re right, Dean – I’m mixing up the full-blown atheists with the “Nones” that I’ve seen reported on.

  6. It is just mind-blogging for me how can people believe that a fifth of the population is transgender or that 3 out of 10 American live in NYC. Just how? They cannot possibly perceive that a fifth of the people around them are transgender, so they believe that elsewhere there are much more of them? Like everybody in California and Oregon? Or what?

    (Also, if they have such an absurd concept of the population of various parts of the country, then no wonder they have no idea what voting result is realistic.)

    1. If the poll is correct then the fact that the surveyed believe that 21% of the population is transgender is a right-winger’s dream because that number magnifies the “transgender threat” that is common in right-wing propaganda. The same goes for the “Muslim threat.”

      1. It’s not the existence of trans people that agitates us nose-picking right-wingers. It’s the vicious depredations of their activists that we see as the threat, a concern not confined to the right.

        Besides, 21% is an oft-quoted number for adolescents and young adults who identify on the non-binary spectrum. A poll respondent anywhere on the political spectrum might bring this number out of his RAM when asked by a pollster to guess at one.

        As yes, radical Muslim ideology is a threat, even if “most Muslims” are not.

        1. “It’s not the existence of trans people that agitates us nose-picking right-wingers.”

          Maybe not you, but would say this in the name of evangelical Christians in general? It is not that modern trans-activism is not irritating and toxic even for me (an evil libtard), but how the Republicans use the issue for their own goals is a different matter. (And yes, unfortunately they are provided with a lot of munition.)

          “Besides, 21% is an oft-quoted number for adolescents and young adults who identify on the non-binary spectrum. A poll respondent anywhere on the political spectrum might bring this number out of his RAM when asked by a pollster to guess at one.”

          This is an explanation worth considering, but I would wager a guess and say that not enough American are aware of that poll to give this result.

          “As yes, radical Muslim ideology is a threat, even if “most Muslims” are not.”

          I think most readers here would agree, but again, I think Historian point is about Republicans magnifying the perception of how big that threat inside the US. (BTW, I think globally it is one of the top threats.)

          1. Especially on Election Day and as a foreigner I speak only for myself. I’m not ignoring you. I’m just ducking your question.

            I must say, though, that this is one of the few places on line or in person where it is possibly to discuss religion without fury. So I’ll just say that it’s a good question.

          2. Re “… It is not that modern trans-activism is not irritating and toxic even for me (an evil libtard)…”

            I vigorously resist conspiracy thinking as much as I possibly can.

            But I confess that in recent years, observing the sheer amount of hullaballoo and noise and high dudgeon and moralizing constantly erupting around the “trans” issue has given me pause. *If* a nefarious state actor were interested in stirring up trouble over a very small proportion of the population, I’d bet a buck or two it would look a lot like this.

            I have no evidence to support that. But the insanity around trans stuff seems positively Kafkaesque to me, sometimes disturbingly Orwellian, and other times disgustingly eschatological/Christian nuttery.

      2. Just proves how the GOP’s main focus is fear mongering and “othering”…when it comes to culture issues, that’s all they talk about, and yet they’re bed-wetting over a very small minority of the population (even when you lump together the LGBTQ, atheists, Muslims and the other “scary people”). And in the majority of red states, the “scary people” are even smaller minorities than what’s listed. “Fear is the mind killer…the little death.”

        1. > Just proves how the GOP’s main focus is fear mongering and “othering”

          Both sides are fear mongering and ‘othering’. It seems like the New Right is operating by portraying their opponents with larger numbers to show that normal Americans (whatever that means) should be afraid of democracy, while the New Left is portraying their opponents with smaller numbers to show that normal Americans should be afraid of elite groups.

          This is a new hypothesis of mine. I’ll have to think about it for a bit, but welcome comments.

      3. I think the worry on the right about the “transgender threat” mostly involves children and the belief that “social contagion” is a real thing.

    1. That was my first thought. People also grossly overestimate the danger of being in a plane crash.

      We think in stories. Tragedies and troubles are more interesting than mundane matters so they get noticed, discussed, and amplified. We evolved in tribes and are cognitively primed to assume that whatever is gossiped about involves occurrences in a small social structure. Lots of stories about minorities means they are well represented. So we overestimate.


  7. Maybe the overestimations come straight from TV. In the past, the life-style represented in at least 26% of TV advertising seemed to reflect incomes over $500,000. And in the last couple of years, the representation of Blacks in TV advertising has increased to maybe 41%. As for New York, if you turn on a TV at random, the chances might be 30% that you will hit one of the innumerable episodes of “Law and Order” and its spin-offs. As for the 30% living in Texas, that stumps me. I have long assumed that 30% live in Springfield, wherever that is, like The Simpsons.

  8. These results reflect very poorly on our educational system. I wonder if a poll of public school teachers would look about the same.

  9. My guess is that the media tends to highlight the activities of minorities—such as Muslims, Jews, and members of the LGBTQ community—which tends to *amplify* their importance. This causes people to overestimate their numbers. People think that 30% of Americans are Jews because issues relating to Jews—such as antisemitism—are often in the news. Similarly, the numbers of people with incomes over $1,000,000 are often vilified in the news (under the heading of “income disparity”) despite their rarity, leaving people with the impression that million-dollar incomes are commonplace.

    In other words, the disparities between perception and reality are probably due to the emphases given in the news and other media, which are then amplified again by the company we keep, where we tend to talk with people of like mind—and reinforce the same biases. Christians hear about those evil atheists, so think that atheism must be more common than it really is. We hear a lot about the military and military veterans in the news and at political gatherings, leading us to overestimate how many people have actually served. And on it goes…

  10. 77% of Americans read a book last year? Americans? Not a chance. Not in this benighted land. I am convinced that stat is just people telling pollsters something aspirational about themselves.

    1. And it could be parents who have read children’s books to their children. Or it can be misconstrued as: “yeah, I read a book…not the entire book, but I read one.”

      1. In the survey about reading recently reported here, the question actually was “read a book whole or in part” or something to that effect.

  11. I like the author’s explanation, at least a little. For example, I personally know only one Jewish family. But I listen to NPR podcasts like This American Life, and Wait, Wait, Don’t Tell Me and many hosts and producers on those shows are Jews. So I might think that I’m rare not knowing very many Jews, so I’d be tempted to overestimate the number. I pay enough attention to know that the percentage is low, but if I didn’t I might guess 5%.

    I’m not sure how anyone could come up with 30%, though.

  12. My social justice warrior daughter recently told me of a link to a video someone had captured of police being mean to some black person. Her summary: “See, dad, police racism *is* systemic”.

    That took a little unwinding. Once indoctrinated in that worldview- they caught her just out of high school – it’s a long way back.

  13. I’ve seen smaller versions of the chart. Every time I see one I’m pleased I guess right on most of them and amazed how off other/most people are. Which gives me no thrill or pride. Nor does the fact that concepts like exponentiality, randomness, etc. are widely misunderstood.

  14. One further point: the infographic includes “are Black” and “are white”. I’m curious whether that was the precise capitalization in the YouGov poll. YouGov is a British market research firm, not a government agency.

  15. Makes sense. Everyone knows that:
    92% of Americans live in New York, Texas, or California;
    80% of Americans are trans, gay, lesbian, or bisexual;
    90% of Americans are muslim, jewish, or atheist.

    (Actual numbers are 24%, 8%, and 6%)

    I do think that 30% of Americans must be gay Jews living in New York, because how else would those things all be 30%?

  16. I would have expected people to overestimate the size of groups they belong to, or are surrounded by every day. I am surprised that this doesn’t seem to play a big role. My hypothesis is that most people are just really bad at making the connection between numbers and reality.

  17. The only substantive point I’ve got on this is to ask if this is a specific thing for Americans, or it’s a general thing for “humans questioned about their society“? Jonathan Dore’s memory at #5 of a similar result from the UK at some point in the past rings a moderate bell for me too – I don’t think this is either a new finding, or a specifically American one. It is within the bounds of poor estimating skills that I remember from exercises in my undergraduate statistics class many years ago – biased by the fact that that “population” had self-selected to be in a class on statistics with a mathematical bias.

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