Optimal Gerrymandering: Sometimes Pack, But Never Crack
研究选区划分的最优策略，发现传统直觉中的“分散”策略从不最优，而应将最坚定的支持者集中在一起，并在信号足够精确时让极端对立选民配对。
Standard intuitions for optimal gerrymandering involve concentrating one's extreme opponents in “unwinnable” districts (“packing”) and spreading one's supporters evenly over “winnable” districts (“cracking”). These intuitions come from models with either no uncertainty about voter preferences or only two voter types. In contrast, we characterize the solution to a problem in which a gerrymanderer observes a noisy signal of voter preferences from a continuous distribution and creates N districts of equal size to maximize the expected number of districts she wins. Under mild regularity conditions, we show that cracking is never optimal—one's most ardent supporters should be grouped together. Moreover, for sufficiently precise signals, the optimal solution involves creating a district that matches extreme “Republicans” with extreme “Democrats,” and then continuing to match toward the center of the signal distribution.