You are a federal court of appeals judge. A defendant calls on you to review his sixty-month prison sentence. The defendant’s actions certainly merit punishment, as he produced and sold over 2,500 false identification documents. His sentence, however, remains in question. Although the lower court sentenced him to sixty months, his sentence was above the range recommended by the advisory United States Sentencing Guidelines (Guidelines), which endorse a sentence ranging between thirty-seven and forty-six months.

Under the Supreme Court’s decision in Gall v United States, you are to determine whether the lower court’s sentence is “reasonable.” In addition, when a sentence falls above or below the Guidelines’ recommended range, you are to examine “the extent of the deviation [from the Guidelines].” When analyzing this deviation, however, you cannot apply “a rigid mathematical formula that uses the percentage of a departure as the standard for determining the strength of the justifications required for a specific sentence.” But, at the same time, you must “ensure that the justification [for the lower court’s deviation from the Guidelines] is sufficiently compelling to support the degree of the variance” because “major” variances from the Guidelines require more support than “minor” ones.

You are left wondering: What does the Supreme Court mean by disallowing the use of “a rigid mathematical formula that uses the percentage of a departure” while still requiring examination of the “extent of the deviation” and “degree of the variance”? As the reviewing judge, must you simply calculate the difference between the lower court’s sentence and the Guidelines in absolute measurements of time? This would mean the defendant, with a prison sentence again of sixty months, was sentenced to only fourteen months above the Guidelines. You may find this measurement particularly persuasive given that the average federal prison sentence nationwide is fifty-seven months. But, perhaps the terms “extent” and “degree” require an examination of the sentence’s relative distance from the Guidelines. Such an analysis would require a percentage calculation. From the top of the Guidelines (46 months), the lower court’s sentence of 60 months demonstrates a 30 percent deviation. Does this calculation change your assessment of the sentence’s reasonableness? When framed in this way, a 30 percent deviation would seem to be a more substantial variance from the Guidelines than 14 months. Does the Supreme Court’s language even require an explicit calculation of the Guidelines variance?

In United States v Castillo, the Seventh Circuit faced this exact scenario. According to the Castillo court, “the relative is generally more important than the absolute.” In support of its view, the Seventh Circuit found it “hard to see how a court can carry out the command of Gall to require a justification ‘sufficiently compelling to support the degree of the variance’— ‘degree’ being a relative rather than absolute measure—without at least considering the percentage deviation.” Like the Seventh Circuit, the Fourth, Sixth, Ninth, and Eleventh Circuits have accepted an interpretation of Gall that supports the use of percentages as a component of reasonableness review in federal sentencing.

An equal number of their sister courts disagree. Citing the Supreme Court’s rejection of “a rigid mathematical formula that uses the percentage of a departure,” the Second, Third, Fifth, Eighth, and DC Circuits disavow percentages. These courts read Gall to demonstrate the Court’s concern with percentages. Moreover, these courts view the introduction of percentage variance calculations into sentencing review as “‘too simplistic’ to effectuate the sentencing purposes of § 3553(a) [the federal sentencing statute].”

This split has provoked a growing, yet overlooked, indeterminacy within federal sentencing jurisprudence. When district courts’ sentences vary from the Guidelines, how should an appellate court evaluate “the extent of the deviation”? At its core, this question raises a fundamental framing problem. As psychologists Amos Tversky and Daniel Kahneman write, “[C]hanges in the formulation of choice problems cause[ ] significant shifts of preference.” Thus, how a court frames a variance matters for purposes of sentencing. An answer that resolves this framing issue not only will address the immediate split dividing appellate courts but also will provide perspective on a broader, ever-evolving issue confronting sentencing law—the allocation of sentencing discretion between district and appellate courts.