Dual Bounds for Redistricting Problems with Non-Convex Objectives

We study optimization models for computational redistricting. We focus nonconvex objectives that estimate expected black voter representation, political representation, and Polsby Popper Compactness. All objectives contain a sum of convolutions with a ratio of variables. The representation objectives are a convolution of a ratio of variables with a cumulative distribution function of a normal distribution, also known as the probit curve, while the compactness objective has a quadratic complication in the ratio. We extend the work of Validi et al. [30], which develops strong optimization models for contiguity constraints and develop mixed integer linear programming models that tightly approximate the nonlinear model, and show that our approach creates tight bounds on these optimization problems. We develop novel mixed integer linear relaxations to these nonconvex objectives and demonstrate the effectiveness of our approaches on county level data

Assigning Backbone NMR Resonances for Full Length Tau Isoforms: Efficient Compromise between Manual Assignments and Reduced Dimensionality

Tau protein is the longest disordered protein for which nearly complete backbone NMR resonance assignments have been reported. Full-length tau protein was initially assigned using a laborious combination of bootstrapping assignments from shorter tau fragments and conventional triple resonance NMR experiments. Subsequently it was reported that assignments of comparable quality could be obtained in a fully automated fashion from data obtained using reduced dimensionality NMR (RDNMR) experiments employing a large number of indirect dimensions. Although the latter strategy offers many advantages, it presents some difficulties if manual intervention, confirmation, or correction of the assignments is desirable, as may often be the case for long disordered and degenerate polypeptide sequences. Here we demonstrate that nearly complete backbone resonance assignments for full-length tau isoforms can be obtained without resorting either to bootstrapping from smaller fragments or to very high dimensionality experiments and automation. Instead, a set of RDNMR triple resonance experiments of modest dimensionality lend themselves readily to efficient and unambiguous manual assignments. An analysis of the backbone chemical shifts obtained in this fashion indicates several regions in full length tau with a notable propensity for helical or strand-like structure that are in good agreement with previous observations

Introduction

This first chapter frames the book through two parallel case studies of how maps and election cycles interact: the Republican congressional gerrymander of Pennsylvania at issue in the 2004 Supreme Court case Vieth v. Jubelirer and the bipartisan map of California’s congressional districts drawn the same year. While Pennsylvania’s gerrymander backfired during the Democratic waves of 2006 and 2008, California’s map, though initially less biased, remained completely unresponsive to shifts in voter preferences throughout the decade. Through these cases, the chapter argues that maps drawn by bipartisan agreement may be just as normatively troubling as partisan maps. Moreover, California resolved this problem of unresponsiveness in 2010 by adopting a nonpartisan commission, while Pennsylvania remained mired in a confusing glut of federal and state litigation. This book argues that California’s path is the wiser one. The chapter concludes with a roadmap of the book’s arguments, evidence, and contributions.</p

Measuring Historical Bias

This chapter briefly examines several existing measures of partisan bias and responsiveness: mean/median difference, partisan symmetry, and efficiency gap. It argues that while these measures tend to be well-adapted when applied to swing states under close electoral conditions, they are inappropriate when applied to noncompetitive states and wave elections. It introduces a new measure referred to as “historically weighted efficiency gap” (HWEG) that estimates bias under the expected range of electoral conditions for any given state. It shows how this measure can be adapted to visualize bias and responsiveness across all plausible election results. The chapter details the data and steps used in the calculation and shows three examples of its use in recently contested gerrymanders (in Pennsylvania, Maryland, and Arizona). The chapter also discusses the strengths and weaknesses of HWEG and describes which states stand out as extreme results under this measure.</p

Gerrymandering or geography? How Democrats won the popular vote but lost the Congress in 2012

This article assesses whether the antimajoritarian outcome in the 2012 US congressional elections was due more to deliberate partisan gerrymandering or asymmetric geographic distribution of partisans. The article first estimates an expected seats–votes slope by fitting past election results to a probit curve, and then measures how well parties performed in 2012 compared to this expectation in each state under various redistricting institutions. I find that while both parties exceeded expectations when controlling the redistricting process, a persistent pro-Republican bias is also present even when maps are drawn by courts or bipartisan agreement. This persistent bias is a greater factor in the nationwide disparity between seats and votes than intentional gerrymandering

Bias and Responsiveness in Partisan Maps

This chapter contrasts the patterns of bias observed between partisan maps in competitive versus noncompetitive states. In large swing states, such as Michigan and Pennsylvania, the efficiency gap curves follow a very reliable pattern, with bias maximized when the national vote is even or slightly favors Democrats, but declining as tides increase. These states also see low competitiveness when the national vote is close, but become very responsive under strong Democratic tides. It contrasts these states with partisan gerrymandering in noncompetitive states, usually overlooked by existing measures, including Tennessee, Indiana, Maryland, and Massachusetts. It finds that partisan maps in noncompetitive states are less aggressive and more defensive than in the swing states and do not attempt to maximize seats the dominant party will win but instead strongly reinforce existing incumbents. This results in maps that appear less biased under normal conditions but will also be less responsive during wave elections.</p

The case of the disappearing bias: A 2014 update to the “Gerrymandering or Geography” debate

This note observes that the pro-Republican bias in the relationship between seats and votes that characterized the 2012 US congressional elections largely disappeared in the 2014 elections, where Republicans won a six-point victory in the national popular vote but only a handful of additional seats. Replicating analysis from an earlier article on the 2012 elections, I find that the source of the decline in bias supports two theories about the effects of gerrymandering and geography on the US Congress. First, bias declined most sharply in states where maps were drawn by Republicans, suggesting that these maps were drawn specifically to maximize seats during a tied national election environment. And second, pro-Republican bias present in bipartisan maps almost entirely disappears, as does the previously observed effect of urbanization on bias, further supporting existing theories about the asymmetric geographic dispersion of partisans

Ground War

Ground War tackles the controversies, litigation, and effects surrounding partisan gerrymandering of the U.S. Congress. The book argues that nonpartisan commissions, not courts, are best equipped to address the issues presented by gerrymandering. It illustrates how existing measures and legal standards are too narrow, being well-adapted to evaluating maps in swing states in close elections but failing to adapt to states or national electoral environments favoring one party. The book demonstrates that the bias and responsiveness of partisan maps are highly sensitive to both the makeup of a state’s electorate and the ephemeral election conditions under which individual elections take place. Therefore efforts to convince courts to adopt legal standards based on any such existing measures are misguided. The book makes its argument through multiple empirical approaches. First, it shows how competition and responsiveness have varied in actual elections as a function of the map-drawing party in interaction with national electoral tides in counterintuitive ways. Second, it uses new measurement techniques to simulate recent maps under a broad range of electoral conditions, revealing differences under varied redistricting regimes and partisan tides and wide variation in the magnitude of bias and responsiveness of partisan gerrymanders. But this does not mean that partisan gerrymandering must be excused as a dilemma without a reasonable remedy. Instead, Ground War argues that nonpartisan commissions, adopted state by state, represent the best alternative to legislative districting, presenting evidence that such commissions foster competitive elections, produce unbiased delegations, and give consideration to representational claims distinctive to each state.</p

Legal Developments and Standards in Partisan Gerrymandering

This chapter explores the legal history and recent court proceedings surrounding partisan gerrymandering, revealing courts to be less than ideal venues in which to sort out competing and possibly noncommensurate claims for fair representation. The chapter begins by framing Justice Kennedy’s search for a universal standard to evaluate partisan gerrymanders in his opinion in Vieth v. Jubelirer. The chapter then details the arguments and decisions in four cases decided in the past few years: Whitford v. Gill, League of Women Voters v. Pennsylvania, Benisek v. Lamone, and Rucho v. Common Cause. For each of the cases, it outlines the unique legal claims by the plaintiff and, where relevant, the arguments accepted and rejected by the court. It then applies a “stylized test” drawn from each case to the facts of the other cases, showing how the standards suggested in one may lead to divergent outcomes in another.</p

Ground war ::courts, commissions, and the fight over partisan gerrymanders /

"Partisan gerrymandering, the drawing of legislative district lines to deliberately favor one political party, has been present and controversial in American politics since before the ratification of our Constitution. Yet in the past couple of decades, parties in power at the state level have developed greater expertise than ever before at redistricting to their own advantage. In Ground War, Nicholas Goedert tackles the controversies, litigation, and effects surrounding partisan gerrymandering of the US Congress. Using multiple empirical approaches and a novel metric to measure the partisan fairness of maps, Goedert argues that nonpartisan redistricting commisions, rather than the US courts, represent the best alternative to legislative redistricting."--Back cove