Efforts to create or promote social problems, particularly when they begin to attract attention, may inspire opposition. Sometimes this involves officials responding to critics by defending existing policies as adequate. Recall that New York police minimized the number of prostitutes in the city, just as the Reagan administration argued that activists exaggerated the number of homeless persons. In other cases, opposition comes from private interests; for example, the Tobacco Institute (funded by the tobacco industry) became notorious for, over decades, challenging every research finding that smoking was harmful.
Statistics play an important role in campaigns to create—or defuse claims about—new social problems. Most often, such statistics describe the problem’s size: there are 10,000 prostitutes in New York City, or three million homeless people. When social problems first come to our attention, perhaps in a televised news report, we’re usually given an example or two (perhaps video footage of homeless individuals living on city streets) and then a statistical estimate (of the number of homeless people). Typically this is a big number. Big numbers warn us that the problem is a common one, compelling our attention, concern, and action. The media like to report statistics because numbers seem to be “hard facts”—little nuggets of indisputable truth. Activists trying to draw media attention to a new social problem often find that the press demands statistics: reporters insist on getting estimates of the problem’s size—how many people are affected, how much it costs, and so on. Experts, officials, and private organizations commonly report having studied the problem, and they present statistics based on their research. Thus, the key players in creating new social problems all have reason to present statistics.
In virtually every case, promoters use statistics as ammunition; they choose numbers that will draw attention to or away from a problem, arouse or defuse public concern. People use statistics to support their point of view, to bring others around to their way of thinking. Activists trying to gain recognition for what they believe is a big problem will offer statistics that seem to prove that the problem is indeed a big one (and they may choose to downplay, ignore, or dispute any statistics that might make it seem smaller). The media favor disturbing statistics about big problems because big problems make more interesting, more compelling news, just as experts’ research (and the experts themselves) seem more important if their subject is a big, important problem. These concerns lead people to present statistics that support their position, their cause, their interests. There is an old expression that captures this tendency: “Figures may not lie, but liars figure.” Certainly we need to understand that people debating social problems choose statistics selectively and present them to support their points of view. Gun-control advocates will be more likely to report the number of children killed by guns, while opponents of gun control will prefer to count citizens who use guns to defend themselves from attack. Both numbers may be correct, but most people debating gun control present only the statistic that bolsters their position.8
THE PUBLIC AS AN INNUMERATE AUDIENCE
Most claims drawing attention to new social problems aim to persuade all of us—that is, the members of the general public. We are the audience, or at least one important audience, for statistics and other claims about social problems. If the public becomes convinced that prostitution or homelessness is a serious problem, then something is more likely to be done: officials will take action, new policies will begin, and so on. Therefore, campaigns to create social problems use statistics to help arouse the public’s concern.
This is not difficult. The general public tends to be receptive to claims about new social problems, and we rarely think critically about social problems statistics. Recall that the media like to report statistics because numbers seem to be factual, little nuggets of truth. The public tends to agree; we usually treat statistics as facts.
In part, this is because we are innumerate. Innumeracy is the mathematical equivalent of illiteracy; it is “an inability to deal comfortably with the fundamental notions of number and chance.”9 Just as some people cannot read or read poorly, many people have trouble thinking clearly about numbers.
One common innumerate error involves not distinguishing among large numbers. A very small child may be pleased by the gift of a penny; a slightly older child understands that a penny or even a dime can’t buy much, but a dollar can buy some things, ten dollars considerably more, and a hundred dollars a great deal (at least from a child’s point of view). Most adults clearly grasp what one can do with a hundred, a thousand, ten thousand, even one hundred thousand dollars, but then our imaginations begin to fail us. Big numbers blend together: a million, a billion, a trillion—what’s the difference? They’re all big numbers. (Actually, of course, there are tremendous differences. The difference between a million and a billion is the difference between one dollar and one thousand dollars; the difference between a million and a trillion is the difference between one dollar and a million dollars.)
Because many people have trouble appreciating the differences among big numbers, they tend to uncritically accept social statistics (which often, of course, feature big numbers). What does it matter, they may say, whether there are 300,000 homeless or 3,000,000?—either way, it’s a big number. They’d never make this mistake dealing with smaller numbers; everyone understands that it makes a real difference whether there’ll be three people or thirty coming by tomorrow night for dinner. A difference (thirty is ten times greater than three) that seems obvious with smaller, more familiar numbers gets blurred when we deal with bigger numbers (3,000,000 is ten times greater than 300,000). If society is going to feed the homeless, having an accurate count is just as important as it is for an individual planning to host three—or thirty—dinner guests.
Innumeracy—widespread confusion about basic mathematical ideas—means that many statistical claims about social problems don’t get the critical attention they deserve. This is not simply because an innumerate public is being manipulated by advocates who cynically promote inaccurate statistics. Often, statistics about social problems originate with sincere, well-meaning people who are themselves innumerate; they may not grasp the full implications of what they are saying. Similarly, the media are not immune to innumeracy; reporters commonly repeat the figures their sources give them without bothering to think critically about them.
The result can be a social comedy. Activists want to draw attention to a problem—prostitution, homelessness, or whatever. The press asks the activists for statistics—How many prostitutes? How many homeless? Knowing that big numbers indicate big problems and knowing that it will be hard to get action unless people can be convinced a big problem exists (and sincerely believing that there is a big problem), the activists produce a big estimate, and the press, having no good way to check the number, simply publicizes it. The general public—most of us suffering from at least a mild case of innumeracy—tends to accept the figure without question. After all, it’s a big number, and there’s no real difference among big numbers.
ORGANIZATIONAL PRACTICES AND OFFICIAL STATISTICS
One reason we tend to accept statistics uncritically is that we assume that numbers come from experts who know what they’re doing. Often these experts work for government agencies, such as the U.S. Bureau of the Census, and producing statistics is part of their job. Data that come from the government—crime rates, unemployment rates, poverty rates—are official statistics.10 There is a natural tendency to treat these figures as straightforward facts that cannot be questioned.
This ignores the way statistics are produced. All statistics, even the most authoritative, are created by people. This does not mean that they are inevitably flawed or wrong, but it does mean that we ought to ask ourselves just how the statistics we encounter were created.
Let’s say a couple decides to get married. This requires going to a government office, taking out a marriage license, and having whoever conducts the marriage ceremony sign and file the license. Periodically, officials add up the number of marriage licenses filed and issue a report on the number of marriages. This is a relatively straightforward bit of recordkeeping, but notice that the accuracy of marriage statistics depends on couples’ willingness