A Partisan Solution to Partisan Gerrymandering: The Define-Combine Procedure Maxwell Palmera, Benjamin Schneerb, and Kevin DeLucab aDepartment of Political Science, Boston University; bJohn F. Kennedy School of Government, Harvard University March 15, 2021 Redistricting reformers have proposed many solutions to the prob- court-ordered non-partisan remedial maps drawn by a lem of partisan gerrymandering, including non-partisan commis- state legislature. All these schemes either require a neu- sions and bipartisan commissions with members from each party. tral third-party actor, trusted by both political parties, Redistricting litigation frequently ends with court- or special-master- to select a fair map, or they necessitate that opposing drawn plans. All of these methods require either bipartisan consen- parties cooperate. However, in today’s hyper-partisan en- sus or the agreement of both parties on the legitimacy of a neutral vironment, there are few independent third-party actors third party to resolve disputes. In this paper we propose a new method for drawing district maps, the Define-Combine Procedure, considered by both sides as able to fulfill this role legiti- that substantially reduces partisan gerrymandering without requir- mately and attempts at cooperation have generated acri- ing a neutral third party or bipartisan agreement. One party defines mony along with maps viewed as partisan or incumbent- a map of 2N equal-population contiguous districts. Then the sec- protecting gerrymanders. In short, intense controversies ond party combines pairs of contiguous districts to create the final continue to surround redistricting, even in states that map of N districts. Using real-world geographic and electoral data, have enacted reforms. we use simulations and map-drawing algorithms to show that this Here we propose a new method for drawing maps, the procedure dramatically reduces the advantage conferred to the party Define-Combine Procedure, which requires neither a neu- controlling the redistricting process and leads to less biased maps tral third party nor bipartisan cooperation. We develop without requiring cooperation or non-partisan actors. a simple framework that allows each party to act in their own partisan self-interest but nonetheless achieves a signif- icantly fairer map than would be drawn by either party on Later this year, every state in the U.S. will begin redrawing its own. We divide the districting process into two stages. their Congressional and legislative district boundaries. Suppose a state must be divided into N equally popu- Many city councils, school boards, county commissions, lated districts. First, one party—the “definer”—draws and other representative bodies will also draw new maps. 2N contiguous, equal population districts. Then, the sec- While redistricting is required by law in order to equalize ond party—the “combiner”—selects contiguous pairs of population across districts, it also creates opportunities districts from the set defined by the first party to create for political actors to benefit certain groups over others. In the final districts. This method produces N equally popu- particular, partisan gerrymandering is used to advantage lated, contiguous districts. By dividing the responsibility one political party over the other, even enabling a party to of drawing districts into two separate stages, in which win a majority of the seats in a legislative chamber without each party retains complete autonomy in their own stage, winning a majority of votes in the election. For example, the parties counteract each other’s partisan ambitions in 2016, Republican candidates for the Wisconsin State while still maintaining considerable flexibility to achieve Assembly won only 45% of the state-wide vote but, due other objectives, including maintaining compactness, con- to partisan gerrymandering, won 63 of 99 seats (64%) and tiguity, and communities of interest. We show that the maintained control of the chamber. Define-Combine Procedure (DCP) produces maps with Gerrymandering hinders democratic representation. large reductions in bias advantaging either political party The public in a representative democracy expects “contin- as compared to maps drawn unilaterally. Using simula- ued responsiveness of the government to the preferences tions based on real-world geographic and electoral data, of its citizens” (Dahl, 1971), a relationship fostered by we assess DCP’s performance in eleven states—to our electoral competition—specifically, the threat of removing knowledge, the first effort demonstrating such improve- from office lawmakers not in step with their constituents ments across a wide variety of geographic and electoral (Canes-Wrone, Brady, and Cogan, 2002). Gerrymander- contexts. ing becomes a critical problem when parties undermine electoral competition by drawing districts that create, Limitations of Current Partisan Gerrymander- enhance or lock in a partisan advantage. ing Fixes Reformers have cycled through a plethora of solutions Reformers have sought to rein in partisan gerrymandering for drawing new district boundaries, including bi-partisan by shifting redistricting authority from partisan legisla- commissions with members from each party, non-partisan tures to nonpartisan independent redistricting commis- geographers, court- or special-master-drawn maps, and sions. State legislatures draw districts in over half of the 1 U.S. states, with the remainder relying on commissions support between parties or appointing a third-party ar- (see Table S1). While redistricting registers higher levels biter to resolve points of difference. A procedure that of citizen satisfaction in states with commissions, commis- sidesteps these common stumbling blocks could reduce sions do not represent a catch-all solution. The absolute the contentious political disputes that accompany de- level of citizen satisfaction with redistricting remains low cennial redistricting, leading to fairer and more quickly- even in commission states (Schaffner and Ansolabehere, produced maps. Second, DCP is a process-based solution 2015). Furthermore, a majority of commission-based to partisan gerrymandering; it does not require courts to states are not actually independent from interference by adjudicate controversial claims of partisan gerrymander- a state legislature, and those that are rely on a mem- ing. As a result, state courts could use this approach ber or members to act neutrally, sometimes touching off to resolve redistricting disputes without having to define controversy—as when the Governor of Arizona sought a standard for identifying partisan gerrymandering in to impeach the independent chair of her state’s com- the first place, thereby reducing lengthy and expensive mission (Druke, 2017). Last of all, states without an litigation. Third, DCP is simple and could be imple- initiative process appear unable or unlikely to implement mented efficiently. Several other proposed solutions have commission-based redistricting, which would require a appealing game-theoretic properties but in practice re- state legislature to cede its authority. quire multiple rounds of bargaining or map drawing and Another common fix to partisan gerrymandering is are difficult or impossible to solve computationally; in through court intervention. While federal judicial inter- contrast, DCP’s two-stage process efficiently produces a vention over partisan gerrymandering claims was effec- complete and valid districting plan. tively closed by the Supreme Court’s decision in Rucho v. Common Cause (2019), anti-gerrymandering efforts in state courts have had some recent success.1 These cases The Define-Combine Procedure rely on state constitutions that either ban partisan ger- rymandering outright or include some version of a “free Suppose a state (or city, school district, or other entity election” clause. Intervention by state courts on a state- engaged in redistricting) with population P needs to be by-state basis will not provide a comprehensive solution, divided into N contiguous single-member districts with however, since many state constitutions place little or no equal population P/N. Elections in the state are contested restrictions on state legislatures’ power to redistrict. More by two parties, A and B. We assume for simplicity that generally, litigation over redistricting remains common- all people in the state vote in all elections, and their place and courts have struggled to adjudicate partisan voting decision is based solely on their personal partisan gerrymandering disputes due to unresolved questions over preference; the makeup of their district and the candidates 2 standards for measuring and comparing partisan gerry- who run have no impact on their vote choice. Let vA manders. SI Appendix A.1 provides a comprehensive be the number of votes in the state for Party A, and discussion of the challenges presented by redistricting vB = P − vA be the number of votes for Party B. For in legislatures and commissions as well as redistricting each district d, let vdA and vdB be the number of votes litigation. in the district for each party. A districting map M is a P Given these challenges, researchers have previously set of N districts, and each district is itself a set of /N proposed solutions to partisan gerrymandering, with some specific voters. Thus, for this framework there is a finite of the most promising drawing inspiration from the cake- set of possible maps M (though it grows extraordinarily cutting problem. While this logic, applied to geography, large as the