PART 1: WHAT DOES IT MEAN TO COUNT?

The German anthropologist Karl Menninger defines counting as “assigning number words to things.” What do we do when we actually count? he asks.

This description of counting makes a certain sense because when we teach kids to count, the first thing we do is drill them on the number words in their language.

It’s easy enough to count the way Menninger says if some grown-up has already told you that everything in the heap is a pea (figure 1). But if I told you that this is a photo of ballots in the 2000 American presidential election, there’d be a question about “hanging chads” and whether those little runty things should be counted as votes.

Figure 1 Peas in Pods

Photo by Bill Ebbesen, https://en.wikipedia.org/wiki/Pea#/media/File:Peas_in_pods_-_Studio.jpg Creative Commons license: CC BY-SA 3.0

So how do we make decisions about what goes in the “heap” of things to be counted in the first place? To find out, I went around the corner to my local bookstore and headed straight for Dr. Seuss. For those of you who don’t know Dr. Seuss, his real name is Theodore Seuss Geisel and he was a physician better known for his fun, easy-to-read children’s books, full of kooky rhymes, made-up words, zany drawings, and irreverence for grown-ups.

When I found One Fish Two Fish Red Fish Blue Fish I was sure I’d found the best learn-to-count book and that it would explain how to count without a grown-up to get you started. ^{Footnote 7} Here’s how it begins:

Did you notice anything peculiar? There are no number words after “two.” We get lots of attributes and wind up with the vague quantity word “a lot.” It’s as though Dr. Seuss has already given up counting after the first line because he’s captivated by something special about each fish.

But let’s continue. Maybe we’ll get beyond two.

Well, no help from Dr. Seuss. He sends us back to the grown-ups.

I think Dr. Seuss meant this book as a message about celebrating differences and having fun together. But for me, One Fish Two Fish is also about the disintegration of counting.

Dr. Seuss never asks, “What makes them all fish? What is fish-ness?” That’s the unanswered question and the paradox we can’t resolve. He ignores differences to count them all as fish at the same time as he celebrates differences to count them all as fish. Here is the existential dilemma of counting: How can we possibly count things if not one of them is like another?

And here is where counting meets power. The only way to count is through intellectual coercion—to force things into categories by ignoring their differences and ultimately, their uniqueness.

By the time we enter graduate school, we’ve lost sight of the intellectual coercion entailed in counting. So let me refresh your memory by taking you back to pre-school. If you look at charts for teaching pre-school kids how to count, you’ll notice that in these elementary charts, the objects in a group are absolutely uniform in size, shape, color, adornments, and even their orientation on the page. Kids don’t have to ignore any differences to count these objects, because there aren’t any.

Once kids have mastered this much, we make it more complicated. We show them pictures of things that are very similar but have some variation. In the Sesame Street book, 1 2 3 Count with Elmo, we get the simple version and a more sophisticated version on the same page. ^{Footnote 8} For the number ‘6,’ the Cookie Monster is shown with six glasses of milk and six cookies (figure 2). For the number ‘9,’ the Count points to nine lightning bolts and nine bats (figure 3). The milk glasses and lightening bolts are exactly the same in size, color, shape and orientation on the page, but no two cookies are alike and no two bats are alike. Some cookies have much more interesting frosting, with pink squiggles, chocolate dots or colored sprinkles, while others are more plain. The bats are different colors, their wings are in different positions, some have their mouths open and some have them closed. And some bats have teeth.

Figure 2 Counting with the Cookie Monster

© 2013, 2017 Sesame Workshop,® Sesame Street.® and associated characters, trademarks and design elements are owned and licensed by Sesame Workshop. All rights reserved. Figure title is the author’s own.

Figure 3 Counting with the Count

© 2013, 2017 Sesame Workshop,® Sesame Street.® and associated characters, trademarks and design elements are owned and licensed by Sesame Workshop. All rights reserved. Figure title is the author’s own.

To a kid, the differences in cookie frosting and bat mouths might be worth considering. “But wait!” the kid thinks to himself. “A grown-up lumped these different things together so I guess I’m supposed to consider them as the same.” Notice that when kids learn to count, they’re not just learning number words and symbols; they’re learning how adults see things.

Another classic type of counting worksheet shows several triangles, rectangles, circles and stars, with items of each shape appearing in different sizes and in different colors—small stars, big stars, red stars, blue stars, and so forth, rather like One Fish Two Fish. Somewhere on the page there are images of shapes and a blank space to fill in the number. Now it’s getting harder to count. There’s still an (imaginary) grown up in the room, but here the kid must make her own decisions. The grown up asks, “How many triangles are there?” or “ How many stars?” Somewhere along the way, the grown up has already taught the kid some clear-cut rules: “If it has three sides, it’s a triangle. Ignore color. Ignore size.”

So, counting isn’t just assigning number words to things. Counting requires classification. Only after classifying can we begin to count. Teaching kids to count is teaching them categorical thinking. “This is a that.”

Counting, to nail the point, is another way of making metaphors. Numbers—those things quantitative analysts love because they are supposedly precise and objective? We construct numbers by solidifying bits and pieces of the swirling miasma that is our real world. In the split second before the number was attached to the thing, the thing could go either way; it could be a this or it could be a that. Numbers are a magic wand that resolves ambiguity into one-ness.

If quantitative reasoning rests on poetic interpretation, on “seeing as,” then the quantitative / qualitative distinction vanishes. And quantitative thinking, like qualitative, is highly cultural. The hard part of counting isn’t memorizing “uno, dos, tres.” The hard part is learning to see the likenesses your culture deems important and to ignore the ones your culture deems incidental (figure 4).

Figure 4 Learning to See the Likenesses Your Culture Deems Important

Credit: Chuck Siler, Carrollton, Texas. February 18, 2011. Title is the author’s own.

Alright, enough with primary school. Let’s come back to the universities where we now sit. We do fancy statistics, regressions, and all that, but we’re just manipulating numbers that came into being by the same process that kids count bats or cookies: grouping things into piles and tagging them with numbers. If we have forgotten the human judgment and cultural conventions entailed in counting, that’s because counting was never taught to us that way. It was never taught to us that way because it was never taught to our teachers that way. Ad infinitum.

Now that we’ve learned how to count, it’s time to start our ethics lessons. Based on what I’ve said so far, here are four thoughts about how to get counting better:

PART 2: HOW DO NUMBERS GET THEIR MEANING?

Numbers get their meaning partly from verbal and visual cues, the kinds of devices Darryl Huff unmasked in How to Lie With Statistics and Edward Tufte does in his books on infographics. ^{Footnote 10} Jane Miller intends the Chicago Guide to Writing about Numbers to play the honest cop to Huff’s burglar, to teach people how to present their data accurately, leaving no room for misinterpretation. Here’s how she advises students to write about their quantitative data:

Oh, really? Do numbers have purposes? No. The people who design measures insert their purposes into the measures. This happens long before you or anyone else starts dressing them up in verbal and visual costumes.

Consider the United Nations indicator of violence against women. ^{Footnote 12} The expert committee charged with designing it decided to create lists of actions that constitute physical, sexual, psychological or economic violence. These lists would then be used to survey women around the globe. Surveyors would ask, “Have you experienced this or that action?” Add up the ‘yesses’ and we’ve got our measure of violence against women in each country.

At an expert committee meeting in 2009, members from Europe, North America, Australia, and New Zealand put forth their ideas about violence, based on gobs of feminist writing and victim surveys in their countries. Women from the Global South didn’t have as much writing or research to draw upon, but they did have plenty of experience with violence. Some Bangladeshi women on the committee put forth another list of items they wished to have included as psychological violence (see table 1).

Some of these things are unimaginable to women who haven’t lived them.

“Expel from the house”: In Western Nepal, some women are forced to sleep outdoors on the wet ground while they’re menstruating, and for three months around the time they give birth.

“Rebuke for giving birth to a girl”: In many places in South Asia, women who don’t produce a male child might be rejected by the husband and his family; beaten, starved, and driven out of their village. A Pakistani woman I know told me she had been married off to a man who turned out to be impotent. To cover his humiliation, he beat her, and his family, of course, took his side and ostracized her. When she eventually fled back to her parents, they discouraged her from seeking divorce because it would bring shame on them, too. She’s now a PhD student at Brandeis.

“Marry other women in addition to existing wife”: Maybe you have an easier time relating to this one, but we’re not just talking affairs or serial marriages here. Dr. Sima Samar, who is now Head of the Afghanistan Independent Human Rights Commission, recalls how her childhood turned miserable when her father took a second wife. She and her mother were relegated to a back room and demoted in dignity, affection, and material things. It was bad enough to be female. Now they were second-class females. ^{Footnote 13}

As you can see, most of the Bangladeshi women’s suggestions didn’t make it into the final indicator (table 2). Of course, many if not all of the items in the United Nations guidelines apply to Bangladeshi women, too. Still, when the numbers come in, they will reveal little about the people whose ideas are not included in the heap of things to be counted.

What do numbers mean? To paraphrase Humpty Dumpty, the numbers mean exactly what the people who design them want them to mean.

Let’s stop here for a couple more ethics lessons:

PART 3: HOW DO NUMBERS GET THEIR AUTHORITY?

For all that’s missing from Menninger’s definition of counting as “assigning number words to things,” he gets one thing right. Assign. What comes into your head when you hear that word? I dare say, homework? Some kind of power? Or perhaps a sense of dread and powerlessness?

Numbers get their authority from people who are able to exert rhetorical and political power to assign words to things and things to categories.

When the delegates at the Constitutional Convention discussed how to count the population in the federal census, the most contentious issue was whether to count slaves as property, in which case their owners would be taxed on them; or to count them as people, in which case the states where they lived would get more representatives in Congress. In the infamous compromise ultimately written into the US Constitution, slaves were counted as three-fifths of a person. In The Federalist No. 54, James Madison defended the rightness of this way of counting:

And yes, I know: Scholars aren’t 100% sure whether Federalist 54 was written by Madison or Hamilton, but most give it to Madison, and since this is the Madison lecture, I will, too.

Scholars often quote these two sentences as if they were Madison’s, and they are, but Madison is playing a cute rhetorical game here. He puts these words in the mouth of an imaginary southerner he creates to argue against the northern position. (Writers can do that sort of thing.) Madison has his imaginary southerner work through a legal analysis to prove that slaves “are considered by our laws in some respects as persons and in other respects as property.”

ETHICS LESSONS

PART 4: HOW CAN COUNTING CHANGE HEARTS AND MINDS?

Much of our social science knowledge comes from asking people what they think, feel, or believe. Look for a minute at some of the questions that researchers have used to find out what whites think about blacks.

In one survey, the interviewers stated that blacks are not as well off as whites and then asked respondents why they thought this might be so. ^{Footnote 16} Here are the possible answers.

• • “Blacks are born with less ability.”

• • “Most blacks who are on welfare could get a job if they really tried.”

• • “If blacks would only try harder, they would be just as well off as whites.”

• • “Black neighborhoods tend to be run down because blacks simply don’t take care of their property.”

• • “Most blacks have a chip on their shoulder.”

• • “Blacks are more violent than whites.”

Here is another question drawn from the National Election Studies. It is designed to get at white people’s sense of feeling threatened by blacks.

I had been reading this scholarship on racism for years, disturbed by its findings but admiring its thoughtful, nuanced research strategies. Then I taught a course on American race politics in Denmark. One night before class, I wondered, as I always do, what my students would make of the readings I had assigned. Suddenly, seeing through young Danish eyes, I felt shocked and ashamed that academics would ask questions like these.

The questions themselves are racist. They presume that race groups are real and everybody knows what they are. They presume that characterizing the behavior and morality of entire groups is possible. The questions stereotype, and in doing so, they teach people that stereotyping is normal and acceptable.

Admittedly, I cherry-picked the most flagrantly racist questions I could find to show you. Most studies of racism include questions that permit respondents to pin the blame on discrimination or structural conditions instead of on blacks as individuals, and to say that blacks aren’t treated fairly.

Nevertheless, asking people to answer questions like these encourages them to buy into stereotyping; they have to buy into it in order to answer. I think we’ve got an example of the Heisenberg Principle here: the measuring process influences the measurement. If counting doesn’t exactly create public opinion, it surely shapes it.

I’m talking here about something deeper than framing effects, that is, how question wording can influence people’s answers. Some of these questions about race educate the public about how to think in the same way that children’s counting charts do, because they provide no opportunity to challenge the lumping assumptions behind them. There is no possibility to say:

• • “I don’t think you can generalize like that.” Or,

• • “I think it’s just plain wrong to stereotype like you’re asking me to do.” Or,

• • “Get out of my face, you racist so-and-so.”

When we talk about these racism studies in my classes, my students at first share my dismay, but eventually, someone comes to their defense. Last semester, a Nigerian woman made the case with an impish twinkle in her eye and an unforgettable question: “I don’t mean any disrespect, Professor, but how else are we going to find out whether white people think Africans live in trees if we don’t ask them?”

I see the point, as the researchers certainly do, too. So let’s ask people if they think Africans live in trees. But let’s also give them opportunities to express incredulity and outrage, or at least disagreement with the premises of the questions. Better yet, by adding some different questions, we might get some white respondents to think about white privilege. For example: in addition to asking whites how likely it is that they’ll be scumped out of a job by a black person, we could ask:

• • Do you know anyone who you think probably got their job more because of their connections than their qualifications? Or,

• • In the place where you work, how much do you think personal relationships with higher-ups influence who gets raises and promotions?

Questions like these might put a chink in the belief that everyone earns whatever goodies they have solely by their own hard work.

We could also ask questions to illuminate how everyone gets help from government.

• • Have you or anyone in your family ever received help from government?

Most people will probably say “no,” so perhaps later probe:

• • Did you or anyone in your family go to public school?

• • Do you have running water in your home? If so, who provides it? How much do you pay for it?

• • Have you or anyone in your family ever received: Social Security, Medicare, Medicaid, or Disability?

While the Affordable Care Act was under debate in 2010, clueless protesters held signs demanding, “Keep Government Hands Off My Medicare,” and “Keep Government Out of Medicaid.” So I know it’s hard to crack deeply held beliefs, but if we want to get counting better, this is what we need to do. Here are three lessons about how.

ETHICS LESSONS

PART 5: ARE THERE SOME THINGS WE SHOULDN’T COUNT?

Once when I was waiting my turn for the vet to see my dog, I overheard him talking with a woman whose dog he clearly thought was obese. They were arguing heatedly about the dog’s diet. “So what should I feed him,” the woman finally yelled in frustration. “Less,” the vet answered.

Sometimes when I’m contemplating Jens Blom Hansen’s question, “How can we get counting right?” I’m tempted to answer, “Don’t.” Two of my top candidates for “Don’t” are counting the value of a life and counting political will. Now, as Jens put it, counting them is here to stay, so take my musings as no-calorie food for thought.

Executive Order 13563 requires government agencies to quantify the expected costs and benefits of any regulation they are considering. ^{Footnote 18} When the benefits include human health and safety, agencies measure them with a concept called “Value of a Statistical Life.” They calculate this value primarily by asking people how much they’d be willing to pay to avoid various risks of death. Mind you, they’re not putting a value on any real person’s life. They’re imputing a value to a human life in the abstract. They project—that means “guess”—the total number of people whose lives might be saved by a regulation and multiply that number by the dollar value of a statistical life. Out the other end of that equation comes the benefit of the regulation—in dollars.

There are many fine treatises for and against valuing lives as a way of deciding on government policy—some of them are no doubt sitting in this room. So here I’ll just note three reasons to say “don’t” based on what we know about counting.

First, in order to count intangibles, we have to fragment them into discrete, observable bits. Things like peas that you can point to and say “one,” “two,” “three.” For some things, such as life, cutting them into countable pieces destroys the meaning and value of the whole. I’m not saying, as many do, that life is “priceless.” Rather, the ways we have to measure its value to us don’t begin to capture what we value about it—never mind that we all value life differently. Not one of us is like another.

Second, the measure is infinitely malleable. The people in charge of an agency can make the analysis come out any way they want, simply by what they choose to include in the cost and benefit estimates, or whether they choose consultants with pro- or anti-government leanings. In 2008, the Environmental Protection Agency cranked some numbers and reduced its working number for the value of life by just under a million dollars. That devaluation rendered some proposed pollution regulations no longer worth their projected cost. ^{Footnote 19} Lower the value of life and a regulation to save lives becomes less of bargain.

Third, as I’ve already said, arithmetic doesn’t resolve value disagreements, it only disguises them.

At the risk of being expelled from the APSA, I’m going to end by questioning what is perhaps the fundamental truth of our discipline (figure 6). Does it make sense to resolve political conflict with elections? To choose leaders and policies by counting votes?

Figure 6 Voting in Lempster, New Hampshire

Photo by Deborah Stone. November 4, 2008.

Barbara Kingsolver’s novel, The Poisonwood Bible, takes place in the Belgian Congo, in the period just before and after independence. ^{Footnote 20} In one scene, we get to see how the idea of majority rule looks to Anatole, a smart young village man. Anatole had been schooled by an American missionary, and he’s now one of the new leaders, responsible for helping manage the first national election in his village. In this passage, Anatole explains his point of view to the missionary’s daughter, who is now his girlfriend:

So what went wrong with Madison’s idea in the Tenth Federalist that a large republic would cure the mischiefs of faction? ^{Footnote 22} What went wrong with the grand hopes after World War II for the end of empire and genocide, and for development and democracy to flourish everywhere? They were all pinned on counting as the way to resolve conflict.

Kingsolver’s character Anatole contrasts tribal ways of making collective decisions with elections:

Anatole’s village is a simpler version of the deliberative democracy many of us wish for. It is, alas, a novelist’s fantasy, so it’s not the answer either. But I do know this: counting is no substitute for talking.