Who says you'll never need algebra in the real world?

06/10/10

The Supreme Court wrestled with just that word problem this year in a case announced on Tuesday. The answer turns on your interpretation of the phrase ''term of imprisonment''. The petitioners in Barber v Thomas interpreted the phrase, found in 18 U. S. C. §3624(b), to mean the length of the sentence as imposed by the judge at trial. Using that method, an inmate would be entitled to a reduction based on the full length of the original sentence. The Bureau of Prisons interpreted the phrase to refer to the length of time actually served. This sounds on the surface like a semantic distinction without a difference, but the math works out to several month extra incarceration under the BoP's interpretation.

The Court held in a 6-3 decision written by Justice Breyer that the BoP's interpretation was correct. Justice Kennedy, who has long argued that American prison sentences are too long and too costly issued a dissent, joined by Justices Stevens and Ginsburg.

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For the sake of everyone who slept through Algebra class in high school, here's how it breaks down. Under the interpretation urged by the petitioners, an inmate serving a 320 month sentence could have his sentence reduced by 1,440 days, just shy of 4 years, for good behavior. The BoP argued that since he didn't actually serve those last 4 years, he can't count that time in calculating the reduction. The BoP's method of calculating the reduced sentence would add back approximately 216 days, or about 7 months. Still with me? If you're confused, the Court didn't fare much better during oral arguments.

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Both methods produce irrational results. Under the method preferred by the bureau, a prisoner serving a sentence of 366 days, the minimum sentence eligible for reduction under the statute, the reduction wouldn't be calculated until day 365 - at which point the prisoner would receive a 54 day reduction that he could no longer use. Under the method urged by the petitioner, he would be released 54 days early, after serving only 312 days - even though it requires a full year of good behavior to qualify for the reduction.

The majority relied on a rather strained mathematical model that took two pages to explain by example, full of assumptions used to simplify the calculations. It assumes that Congress intended for the calculation of the good behavior credit to be more complicated than understanding the federal tax codes. The dissent urges a method of calculation that can be done without an advanced degree in mathematics, but requires us to believe that each year is composed of 311 days plus and additional 54 days that can be made to disappear through good behavior. It has the benefit of simplicity but requires us to suspend disbelief for a time. The real argument made by Justice Kennedy in the dissent is in the opening paragraph where he says ''... if the only way to call attention to the human implications of this case is to speak in terms of economics, then it should be noted that the Court's interpretation comes at a cost to the taxpayers of untold millions of dollars…The interpretation the Court adopts, moreover, will be devastating to the prisoners who have behaved the best and will undermine the purpose of the statute.''

Now if only my high school math class had been this interesting...