Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- winner-take-all single-member districts -- both enables substantial partisan gerrymandering and constrains `fair' redistricting, preventing proportional representation in legislatures. We study the design of \textit{multi-member districts (MMDs)}, in which each district elects multiple representatives, potentially through a non-winner-takes-all voting rule. We carry out large-scale analyses for the U.S. House of Representatives under MMDs with different social choice functions, under algorithmically generated maps optimized for either partisan benefit or proportionality. Doing so requires efficiently incorporating predicted partisan outcomes -- under various multi-winner social choice functions -- into an algorithm that optimizes over an ensemble of maps. We find that with three-member districts using Single Transferable Vote, fairness-minded independent commissions would be able to achieve proportional outcomes in every state up to rounding, \textit{and} advantage-seeking partisans would have their power to gerrymander significantly curtailed. Simultaneously, such districts would preserve geographic cohesion, an arguably important aspect of representative democracies. In the process, we open up a rich research agenda at the intersection of social choice and computational redistricting.
翻译:每个有代表性的民主必须规定一个选民选择其代表的机制。美国最常用的机制 -- -- 赢者-所有单一成员选区 -- -- 都能够进行大规模的分析,同时能够进行大量的党派干预,并限制`公平'重新划分,防止立法机构中出现比例代表。我们研究“textit{多成员区(MMDs)”的设计,其中每个区可以选举多个代表,有可能通过非赢者-全票投票规则。我们为具有不同社会选择功能的MMDs下美国众议院进行大规模分析。根据有逻辑绘制的地图,可以优化党派利益或相称性。这样做需要有效地将预测的党派结果 -- -- 在不同多赢者社会选择功能下 -- -- 纳入一种最优于各种地图组合的算法。我们发现,如果三个选区使用单一可转移的选票,公平独立委员会将能够在每个州取得比例结果,直至四舍、通票{和}追求优势的党派代表院将拥有其权力,可以大大削弱党派利益或相称性。这样,这样需要有效地将预测的党派结果纳入一个重要、相互交汇的地域议程。