Few aspects of elections generate more controversy than the decennial redistricting of federal, state, and local offices. Because of the conflict inherent in designing new districts, since the redistricting revolution began half a century ago, challenges to maps have been among the most common aspects of election law heard by the courts. Recasting the political landscape presents the opportunity to alter the fortunes of political parties and open the way for those under-represented in the legislature to win seats. By deftly allocating supporters and opponents, a party may succeed in winning a much larger share of the seats than its percentage of the votes. In the most extreme case, clever mapping of single-member districts could enable a party to win virtually all of the seats with little more than a majority of the vote. In some situations, strategic placement of their supporters allows a party to win a majority of the seats with fewer than half the votes. In contrast, political systems that use proportional representation keep the votes-to-seats ratio near one by awarding each party a share of seats in the legislature roughly equal to its share of the vote.1