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Watch That Denominator

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One of the favorite tricks of mathematical prestidigitators is to keep the audience's eyes on the numerator while slipping something fishy into the denominator, producing a startling ratio. This article by Terry Woster in the Argus Leader (Sioux Falls, SD) contains a good example.

Almost one of every nine persons sentenced to death since 1977 has asked, as Elijah Page did in South Dakota last summer, to have all legal appeals ended and the execution carried out, a University of Colorado death penalty scholar says.

Those of us working the field immediately suspect that so-called "volunteers" aren't that common, and indeed they are not. It turns out the numerator of 126 volunteers is placed over a denominator of 1083 executions to yield the 1/9 ratio. But there is a vast difference between the number of people sentenced to death and the number executed. It's about a factor of 7. See BJS, Capital Punishment 2005. So that 1/9 is really more like 1/63.

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This is the same apples and oranges trick that is done when abolitionists compare the number of people allegedly exonerated from Death Row with the number of convictions. Obviously, the appropriate comparison is between the number of alleged exonerees and the number of actual death sentences imposed.

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