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Abortion Rights and the Largeness of the Fraction ⅙

The most important abortion rights Supreme Court case in decades may hinge on the answer to a seemingly trivial question—is ⅙ a large fraction?

Last year, the Fifth Circuit answered by stating, with minimal analysis, that ⅙ is not a large fraction. The impact of this assertion is potentially enormous. The state of Texas’s recently‐enacted abortion regulations—which require doctors who work at abortion clinics to obtain admitting privileges at local hospitals and mandate that clinics where abortions are performed meet the exacting standards of ambulatory surgical centers—were found to be constitutional. As a result, a state that used to have over 40 clinics could have only 8 or 9.

In this article, we challenge the Fifth Circuit’s description of the fraction ⅙. We do so by empirically testing whether individuals consider ⅙ a large fraction in different scenarios. We find that the Fifth Circuit’s understanding of ⅙ is at odds with the common semantic understanding of the fraction. In particular, our study produces four conclusions that are inconsistent with the Fifth Circuit’s analysis:

(i) In particular scenarios, an overwhelming majority of people characterize ⅙ as a large fraction.
(ii) The expected outcome of a scenario influences whether people
describe ⅙ as a large fraction.
(iii) A large majority of people can sometimes consider fractions larger than ⅙ to be small, and fractions smaller than ⅙ to be large.
(iv) In politically‐charged scenarios, political orientation can affect whether a person perceives ⅙ as a large fraction.

What this means for the case before the Supreme Court is quite simple—that the Fifth Circuit’s analysis of whether ⅙ is a large fraction has no basis in the everyday understanding of the term “large fraction” or of the fraction ⅙ itself. When the Supreme Court decides this case, it should heed this conclusion and offer a more thoughtful analysis of this potentially decisive question.

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