Americans and Innumeracy

by John Sides on January 8, 2012 · 13 comments

in Public opinion

In the Wall Street Journal, Carl Bialik mentions some of my research with Jack Citrin in a piece called “Americans Stumble on Math of Big Issues”:

Political scientists John Sides of George Washington University and Jack Citrin of the University of California, Berkeley, hypothesized in a working paper that supplying Americans, who typically overestimate the number of immigrants and illegal immigrants among them, with correct numbers would reduce the perceived threat of immigration and change their views. Instead, getting the right number reinforced their views, and even increased their support for letting fewer immigrants into the U.S.

There’s a lot of political science research cited in the piece—including some by James Kuklinski, Arthur Lupia, and others.

However, the quote above prompts Felix Salmon to write:

Which only goes to prove how out-of-touch political scientists can be. Not only are people naturally innumerate, but more generally you can’t argue people out of positions that they weren’t argued into.

Perhaps it’s silly of me to get worked up over something Salmon tossed off on his Tumblr.  But I am.  The ad hominem “out of touch” is what did it.  Really, the laziest thing one can say about scientific research is some version of “That study confirmed what I already thought so it’s a stupid study.”

But the substance of his remarks about innumeracy is wrong too.  And it’s important to say why.

First, are people “naturally innumerate”?  Consider their knowledge of politically relevant numbers.  Citrin and I show that citizens of many countries overestimate the percent of the population who is foreign-born.  Indeed, people tend to overestimate the proportion of the population that belongs to most minority groups (blacks, Latinos, gays, Jews, people on welfare, etc.).  And many Americans get specific policy details wrong: how many people pay the estate tax and the proportion of the budget spent on foreign aid, for example.  And some other things too.

But, on average, Americans are pretty accurate in their estimates of average income.  Eric Lawrence and I have also found that they are fairly accurate in their estimates of the percent of the population with college degrees and in their estimates of the unemployment rate.  Stephen Ansolabehere, Marc Meredith, and Erik Snowberg also find that their estimates of gas prices are pretty accurate.

In short, innumeracy is not a “natural” state.  The extent of innumeracy varies, depending on what numbers you’re asking people to estimate.

Second, when you correct misperceptions, does it matter?  Salmon suggest that it couldn’t: people can’t be argued out of positions that they weren’t argued into.  And there is much academic literature to back him up.  Indeed, if Salmon had read Citrin’s and my research, he would see that we are “in touch” enough to discuss that very expectation in detail.  We write:

In this case, there are good reasons to believe that attitudes toward minority groups are in fact less susceptible. Instead these attitudes may prove relatively stable despite any new, and more accurate, information.

And we go on to say why.

But there is also literature that finds the opposite: that information does change misperceptions and thereby attitudes.  I’ve previously mentioned my findings about public opinion and the estate tax: telling people that only a relatively few and relatively rich people pay this tax does reduce opposition to the tax.  Martin Gilens finds that telling people the correct fraction of the budget spent on foreign aid reduces their desire to cut it.  Similarly, he finds that telling them that the crime rate—another thing people tend to overestimate—is declining reduces their desire to spend money on prisons.

So again, the results vary.  Whether and how much is the public affected by correct information?  It seems to depend, although we don’t yet know on what.  But it’s not correct to suggest that the mere possibility is laughable.

Ultimately, I’d say the problem is not that political scientists like Jack Citrin and me are “out of touch” with the obviously correct ideas of Felix Salmon.   The problem is that Salmon isn’t “in touch” with political science.


Jonathan Ladd January 8, 2012 at 12:49 am

Scientific findings that match our priors are obvious/trivial. And those that contradict our priors we usually don’t believe because you can almost always poke some holes in the research design or execution. The lesson: motivated reasoning afflicts us all.

James W. January 8, 2012 at 8:39 am

Don’t worry, just a few more years and you ivory tower pieces of s—- will have succeeded in electing a new people who don’t care about criminal hispanic immigrants because they are all criminal hispanic immigrants.

James W. January 8, 2012 at 8:49 am

There’s several very obvious reasons why people overestimate the numbers of immigrants.

1. Immigrants are much more disruptive/visible

2. If you live near a major metro area, the percentage of immigrants is much higher than the national average, so you can hardly blame someone who sees mostly brown people on a daily basis for not remembering that Iowa for example is much less plagued by diversity.

3. Media. A continuous barrage of left-wing propaganda about “the changing face of the nation” plus extremely generous media coverage for “hispanic activists” plus mandated politically correct multikult advertisements. From watching CNN for a day, including commercials, you might reasonably expect that the USA was about 30% black, 30% hispanic, 25% white, 5% other. Obviously this is the wet dream of the establishment but we are not there yet thank god.

James W. January 8, 2012 at 8:53 am

Finally (and I am TRULY sorry for comment diarrhea) — political scientists ARE out of touch. You discuss your fellow citizens in the abstract as if “Americans” is not a group you feel you belong to. You also tend to live very near to Universities, such places (whether college towns or major metro cities) are quite different from where “the rest of america” lives.

Ben Donahower January 8, 2012 at 9:33 am

I second the media!

People estimate these types of numbers, mostly, based on their life experience. It makes sense that people can identify an average person’s salary but not the percentage of a particular minority population with this in mind.

I responded to a question on Quora similarly. The user asked why the left is obsessed with Sarah Palin. I said the media is obsessed with Sarah Palin and that translates into a distorted awareness of her. To support my view, I did a couple Google News searches:

I just searched in Google news for ‘sarah palin’ and ‘joe biden.’ The search on Sarah Palin found 29,946 results. The Joe Biden search found only 4,802 news stories.

Without context to news coverage people will make errors in estimation. Who would have thought that, to use another example, there are more Buddhists in this country than Muslims, but there are:

Or, using the same data, why there was so much news coverage over whether to say merry Christmas or happy holidays when aside from some certain neighborhoods and regions an astronomical number of people celebrate Christmas particularly when you account for the secular people that also celebrate it as a cultural holiday?

In addition to these isolated religious issues that I brought up, essentially all other hot button issues or political wedge issues are included: diversity, immigration, gun rights, abortion, and homosexuality with misconceptions from the right and the left.

gman January 9, 2012 at 8:02 pm

“left wing propoganda”..that give cover for major companies to acutally recruit from south of the border to keep wages down. Sure the dems won’t turn down the votes and reps won’t turn down a chance to keep their foot on the throat of native workers.

mrrunangun January 8, 2012 at 1:08 pm

When discussing the nature of the “average American’s” experience of, or attitude toward, or opinion of an object it would be helpful to have some idea of how representative the average may be of the whole. If the bell curve’s peak is shallow and it’s tails long and fat, the average is unrepresentative. What is the distribution of “numeracy” , favorability of experience with immigrant groups, attitudes toward rival ethnic groups, etc. The experiences of members of America’s multiracial educated professional world (including professors) with members of other ethnic groups is probably much more favorable than the experiences of members of the Teamsters or a Laborers’ Local.

John Sides January 8, 2012 at 10:28 pm

mrrunangun: If you click through the links in the blog post, you will see a lot of histograms and other graphs that demonstrate the shape of the distribution of these estimates.

RobC January 8, 2012 at 4:23 pm

I believe Salmon has made the mistake of conflating innumeracy (inability to deal with mathematical concepts and methods) and simple ignorance about some facts that involve numbers, and John Sides adopts Salmon’s mistaken terminology. The Wall Street Journal article concerned numerical misperceptions and, rightly, never mentioned numeracy or innumeracy. Sometimes, of course, innumeracy among journalists causes them to print statements that are wrong or misleading, fostering the kind of ignorance about numerical facts among the general public that we all deplore.

John Sides January 8, 2012 at 10:27 pm

RobC: Those are certainly two different ideas, but the literature uses “innumeracy” to refer to both (for better or worse) — so I adopt that convention here. In part, this is because the two things tend to go together. For example, ignorance about racial/ethnic demographics leads to estimates of the % black, white, Asian, and Latino that, on average, sum to >100%.

Orlando January 9, 2012 at 8:37 pm

Well, in this particular case, since Latino may also be white/black/Asian (or any combination), adding up to more than 100% is correct :) Actually, since many people could classify themselves/be classified as more than one race (Obama, Tiger Woods, … just to get famous examples), more than 100% would make perfect sense :)

Richard H. Serlin January 8, 2012 at 11:51 pm

“In this case, there are good reasons to believe that attitudes toward minority groups are in fact less susceptible. Instead these attitudes may prove relatively stable despite any new, and more accurate, information.”

Yet, people so often underestimate time, persistence, and relentlessness. How stable have race attitudes been over the last 50 years? Who’s in the Whitehouse?

John Griffin January 10, 2012 at 1:03 pm

If you are saying that innumeracy does not drive policy attitudes as much as policy attitudes drive innumeracy I think you are probably correct.

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