Read more of our coverage of ​Whole Woman’s Health v. Hellerstedt​ here.

This article is based on a new study published in the University of Pennsylvania Law Review Online. 

If we told you that one-sixth of pregnancies in the United States would result in the death of the pregnant person, would you consider that number a large fraction?

How about if one-sixth of your life savings were wiped away in a banking error? Would you think one-sixth was a large fraction then?

When the Supreme Court hears oral arguments Wednesday in Whole Woman’s Health v. Hellerstedt, the most important abortion case before the Supreme Court in more than two decades, the resolution of the case may just come down to how the justices regard that fraction.

At issue in the case is a Texas law that, among other provisions, would require doctors who perform abortions to have admitting privileges at local hospitals and require abortion clinics to meet the exacting requirements of ambulatory surgical centers. If the law is allowed to go into effect, advocates say, all but nine or ten of the state’s abortion clinics will close. About 900,000 Texas women of reproductive age would have to travel more than 150 miles each way in order to reach one of those remaining clinics. With about 5.4 million women of reproductive age in the state, that would mean one-sixth of Texas’ women would face a serious obstacle in obtaining an abortion.

Why does it matter what fraction of women are affected? In a line of cases starting with Planned Parenthood v. Casey in 1992, the Supreme Court and other federal courts have ruled that an abortion restriction will be found unconstitutional if it constitutes an “undue burden” on a woman’s right to choose. The Court explained further that an undue burden exists when the law is a substantial obstacle for a “large fraction” of people who are subject to that restriction.

Casey involved a Pennsylvania law that would have required married women to notify their husbands before they got an abortion. The Court reasoned that this provision only really affected women who were not in trusting relationships with their husbands. Based on the evidence before the Court, many of those women were in abusive relationships—so for an unspecified large fraction of them, requiring them to tell their husbands would be a substantial obstacle. Thus, this part of the law was struck down as unconstitutional.

In Whole Woman’s Health, however, the Fifth Circuit Court of Appeals upheld the law, concluding that one-sixth is “nowhere near” a large fraction; in a separate case, the same court ruled that a restriction that does not fall on the “vast majority” of women can never be a large fraction. Whether the Supreme Court agrees with the Fifth Circuit on this issue could very well determine the outcome of Whole Woman’s Health.

So is one-sixth a large fraction? We considered this question in a new study we published in the University of Pennsylvania Law Review. In it, we argue that the Fifth Circuit ignored the common understanding of one-sixth and the concept “large fraction.” The Supreme Court needs to take this study’s findings into consideration.

In our study, we distributed an online questionnaire (which you can take at the link) to potential respondents through Amazon’s Mechanical Turk system. The questionnaire included a few questions about respondents’ demographic characteristics and political orientation. Of primary interest, however, were 12 scenarios that we asked respondents to read. Each scenario featured the fraction one-sixth, and after each, we asked respondents, “In this scenario, do you consider one-sixth to be a large fraction?” Respondents could answer “yes” or “no.” We randomized the order in which the scenarios were presented.

We ended up with a sample of 504 individuals. The sample was heterogeneous: 76 percent of participants self-identified as white, 9 percent Asian or Pacific Islander, 7 percent African-American, 3 percent Hispanic or Latino, and 5 percent mixed-race or other. Fifty-seven percent of respondents were male. They ranged in age from 18 to 76 years, with almost 70 percent being between 25 and 44 years old. What did we find?

First, it is easy to invent hypothetical scenarios in which the vast majority of people will describe one-sixth as a large fraction. When presented with a scenario in which one-sixth of tablets in a bottle of Tylenol were laced with the poison cyanide, 91 percent of respondents reported that one-sixth was a large fraction. When the scenario involved your boss requiring you to donate one-sixth of your take-home pay to her daughter’s elite private school, 93.5 percent of respondents did so.

Second, we found that changing key elements of otherwise similar scenarios can result in large differences in the proportion of respondents who described one-sixth as a large fraction. For example, we presented two scenarios, each of which involved a local business with 100 employees working at its main office. In one scenario, we said that the employees normally arrive on time, but that one day, one-sixth of them arrived to work late. In the alternate scenario, we said that one-sixth of employees of that business were killed one day in separate individual car accidents. When the scenario involved employees being late, only 28 percent of respondents described one-sixth as a large fraction; when it involved employees being killed in car accidents, fully 92 percent did so. Clearly, whether one-sixth is a large fraction depends heavily upon the baseline expectation in the scenario in which it is presented.

We also presented two politically charged scenarios, and examined how respondents’ tendency to describe one-sixth as a large fraction in these scenarios depended upon their own political orientation. One scenario mirrored closely the law at issue in Whole Woman’s Health: A state enacts a law that forces abortion clinics to close, and as a result, one-sixth of women of reproductive age would have to travel 150 miles or more to get to a clinic that remained open. A companion scenario involved a state law that forced gun stores to close, leaving one-sixth of the state’s adult residents 150 miles or more away from a gun store that remained open. Overall, 76 percent of respondents agreed that one-sixth was a large fraction in the abortion clinic scenario, whereas 52 percent did so in the gun store scenario.

What was most interesting, however, was how these responses varied according to respondents’ political orientation. We asked respondents to place themselves along a five-point scale, from very conservative to very liberal. In the abortion clinic scenario, 88 percent of people who described themselves as very liberal, compared to 48 percent of people who described themselves as very conservative, agreed that one-sixth was a large fraction. The pattern was reversed in the gun store example: 38 percent of people who said they were very liberal, versus 62 percent who said they were very conservative, described one-sixth as a large fraction in that scenario. 

These results would not be surprising to a linguist. The adjective “large” has no absolute meaning, and becomes meaningful only in relation to a comparison group or baseline set of expectations. The basketball player Manute Bol is a large person, compared to other people, or even other NBA players. But a redwood tree of the same size would be considered small, and a planet the size of Manute Bol would be … not a planet at all.

What does all of this mean for Whole Woman’s Health? The Court has never specified what exactly a “large fraction” is under the Casey test, so the everyday English understanding of the phrase matters. With that in mind, the Fifth Circuit’s claims—that only a “vast majority” can count as a “large fraction” and that one-sixth “nowhere near” qualifies—is clearly at odds with common usage.

As our questions about political orientation indicate, the Supreme Court justices should be particularly careful to not to use superficial arguments to provide intellectual cover for their own moral beliefs or political views about abortion.

In its consideration of the case, the Court must provide a more sophisticated analysis that recognizes not only that one-sixth clearly can be a large fraction in some scenarios, but also that the determination has much to do with assumed expectations and values. In particular, if the justices value a woman’s constitutional right to choose to have an abortion, then one-sixth should be seen as a large fraction—because our baseline expectation should be that few people have their constitutional rights denied.