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As the
U.S. Supreme Court deliberates over whether a mathematical formula dubbed the "
Efficiency Gap" should be used to detect unconstitutional partisan gerrymandering, this new theorem proves that in some cases, the Efficiency Gap will flag only bizarrely shaped districts as being constitutional.
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The researchers pointed to three general criteria that are followed in the U.S. today for drawing the boundaries of districts. Only the first comes from the Supreme Court: Each district should contain roughly equal represented populations, a criterion known as "one person, one vote," which results from the Court's interpretation of the Equal Protection Clause to the Constitution.
The second criterion is a law in some states, but not all: Districts should be compact in shape. They shouldn't look weird to the eye, like the salamander-shaped district Elbridge Gerry drew in 1812.
There's no legal requirement for the third criterion, and the case currently before the Supreme Court asks the Court to make such a requirement: Districts should balance the votes of people belonging to different political parties in a way that's roughly equal.
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In short, Mixon and Alexeev's new theorem proves that sometimes only two of these three criteria can be satisfied using the Efficiency Gap methodology. In those cases, when districts are drawn to contain equal numbers of voters and balance between the parties, the resulting shapes are highly asymmetrical. They look gerrymandered, but they're not.
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