Optimal gerrymandering: Sometimes pack, but never crack

• 成果类型: Article
• 署名作者: Friedman, John N.; Holden, Richard T.
• 署名单位: University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
• 刊物名称: AMERICAN ECONOMIC REVIEW
• ISSN/ISSBN: 0002-8282
• DOI: 10.1257/aer.98.1.113
• 发表日期: 2008
• 页码: 113-144
• 关键词: voter

摘要

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.