No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Base Rate Neglect and the Diagnosis of Partisan Gerrymanders
... For completeness, we consider a series of alternative outcomes which measure the partisan bias of redistricting plans. We first consider an alternative to the efficiency gap, the dilution asymmetry (Gordon and Yntiso, 2024). ...
Political actors frequently manipulate redistricting plans to gain electoral advantages, a process commonly known as gerrymandering. To address this problem, several states have implemented institutional reforms including the establishment of map-drawing commissions. It is difficult to assess the impact of such reforms because each state structures bundles of complex rules in different ways. We propose to model redistricting processes as a sequential game. The equilibrium solution to the game summarizes multi-step institutional interactions as a single dimensional score. This score measures the leeway political actors have over the partisan lean of the final plan. Using a differences-in-differences design, we demonstrate that reforms reduce partisan bias and increase competitiveness when they constrain partisan actors. We perform a counterfactual policy analysis to estimate the partisan effects of enacting recent institutional reforms nationwide. We find that instituting redistricting commissions generally reduces the current Republican advantage, but Michigan-style reforms would yield a much greater pro-Democratic effect than types of redistricting commissions adopted in Ohio and New York.
Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This note explores some of its mathematical properties in light of the fact that it reduces to a straight proportional comparison of votes to seats. Though we offer several critiques, we assess that EG can still be a useful component of a courtroom analysis. But a famous formula can take on a life of its own and this one will need to be watched closely.
Significance
Markov chains are simple mathematical objects that can be used to generate random samples from a probability space by taking a random walk on elements of the space. Unfortunately, in applications, it is often unknown how long a chain must be run to generate good samples, and in practice, the time required is often simply too long. This difficulty can preclude the possibility of using Markov chains to make rigorous statistical claims in many cases. We develop a rigorous statistical test for Markov chains which can avoid this problem, and apply it to the problem of detecting bias in Congressional districting.
With little fanfare, the electoral advantage enjoyed by US representatives has fallen over the past several elections to levels not seen since the 1950s. The incumbency advantage has diminished in conjunction with an increase in party loyalty, straight-ticket voting, and president-centered electoral nationalization, products of the widening and increasingly coherent partisan divisions in the American electorate. Consequently, House incumbents now have a much harder time retaining districts that lean toward the rival party. Democrats had been the main beneficiaries of the denationalization of electoral politics that had enabled the incumbency advantage to grow, and they have thus been the main victims of the reemergence of a more party-centered electoral process. Republicans enjoy a long-standing structural advantage in the distribution of partisans across districts, so this trend has strengthened their grip on the House even as they have become less competitive in contests for the presidency.
For both two-party and multiparty elections we construct a baseline standard for fair seat proportions based on three intuitive assumptions about plurality voting systems. We show that such systems are inherently biased against minority parties irrespective of political geography and are thus incompatible with the ideal of proportional representation. The construction produces sensible theoretical and empirical results when applied to U.S. and Canadian elections, and it is consistent with baseline standards produced by certain simulation methods. We apply the standard to detect partisan gerrymanders in a simple way that handles edge cases appropriately and flags expected real maps as problematic.
Legislative redistricting is a critical element of representative democracy. A number of political scientists have used simulation methods to sample redistricting plans under various constraints in order to assess their impact on partisanship and other aspects of representation. However, while many optimization algorithms have been proposed, surprisingly few simulation methods exist in the published scholarship. Furthermore, the standard algorithm has no theoretical justification, scales poorly, and is unable to incorporate fundamental constraints required by redistricting processes in the real world. To fill this gap, we formulate redistricting as a graph-cut problem and for the first time in the literature propose a new automated redistricting simulator based on Markov chain Monte Carlo. The proposed algorithm can incorporate contiguity and equal population constraints at the same time. We apply simulated and parallel tempering to improve the mixing of the resulting Markov chain. Through a small-scale validation study, we show that the proposed algorithm can approximate a target distribution more accurately than the standard algorithm. We also apply the proposed methodology to data from Pennsylvania to demonstrate the applicability of our algorithm to real-world redistricting problems. The open-source software package is available so that researchers and practitioners can implement the proposed methodology.
The relationship between votes and seats in the legislature lies at the heart of democratic governance. However, there has been little previous work on the downstream effects of partisan gerrymandering on the health of political parties. In this study, we conduct a comprehensive examination of the impact of partisan advantage in the districting process on an array of downstream outcomes. We find that districting bias impedes numerous party functions at both the congressional and state house levels. Candidates are less likely to contest districts when their party is disadvantaged by a districting plan. Candidates that do choose to run are more likely to have weak resumes. Donors are less willing to contribute money. And ordinary voters are less apt to support the targeted party. These results suggest that gerrymandering has long‐term effects on the health of the democratic process beyond simply costing or gaining parties seats in the legislature.
We study a partially identified linear contextual effects model for ecological inference, and we describe how to perform inference on the district level parameter averaging over many precincts in the presence of the non-identified parameter of the contextual effect. We derive various bounds for this non-identified parameter of the contextual effect, from the tightest possible, to ones that may be more practical for applications. This may be regarded as a first attempt to limit the scope of non-identifiability in linear contextual effects models. As an application, the linear contextual model implies a "regression bound" for the district level parameter of interest, which can be intersected with the model-free bound of Duncan and Davis (1953) to obtain a shorter width than using the model-free bounds alone, at varying confidence levels.
In 2016, a Wisconsin court struck down the state assembly map due to unconstitutional gerrymandering. If this ruling is upheld by the Supreme Court's pending 2018 decision, it will be the fist successful political gerrymandering case in the history of the United States. The efficiency gap formula made headlines for the key role it played in this case. Meanwhile, the mathematics is moving forward more quickly than the courts. Even while the country awaits the Supreme Court decision, improved versions of the efficiency gap formula have been proposed, analyzed and compared. Since much of the relevant literature appears (or will appear) in law journals, we believe that the general math audience might find benefit in a concise self-contained overview of this application of mathematics that could have profound consequences for our democracy.
Recent scholarship has documented the advantages of a new measure of partisan gerrymandering: The difference in the parties' wasted votes, divided by the total number of votes cast. This measure, known as the efficiency gap (EG), can be calculated directly from aggregate vote totals, facilitating comparison of the severity of party gerrymandering across states and time. In this article, we conduct the first analysis of the EG's effects on legislative representation and policymaking in the states. We first show that the partisan outcome of legislative elections has important causal effects on the ideological representation of individual districts, the ideological composition of legislative chambers, and the conservatism of state policymaking. We then show that variation in the EG across state-years is associated with systematic differences in the ideological location of the median state legislator and in the conservatism of state policies. These results suggest that partisan gerrymandering has major consequences not only for who wins elections but for the political process as a whole. Keywords: redistricting, gerrymandering, state politics, representation, legislatures
Partisan unfairness is easily detected when the statewide vote is equally divided between two parties. But when the vote is not evenly divided, even the determination of which party is disfavored becomes controversial. This article examines the ideal fair outcome in a two party single member district system when the statewide vote is not equally divided. It is shown that equal voter empowerment, implied by readings of the First Amendment (Shapiro v. McManus and Whitford v. Nichol), requires that the fraction of seats be proportional to the fraction of the statewide vote. However, strict proportionality conflicts with the single member district system, so alternative approaches are explored. Generalized party inefficiency and voter effectiveness are defined and shown to encompass many possibilities for an ideal fair seats-votes function. The best choice is fundamentally determined by the degree of geographical heterogeneity of voters of like mind. Based upon historical election results, it appears that a good approximation to a normative seats-votes function of the American system of single member districts should have competitiveness (aka responsiveness) roughly twice as large as proportionality. This is consistent with the method employed by the plaintiffs in Whitford v. Nichol. This method is also basically consistent with the claim of the plaintiffs in Shapiro v. McManus, although in this case gerrymandering is better exposed by examining symmetry.
While conventional wisdom holds that partisan bias in US legislative elections results from intentional partisan and racial gerrymandering, we demonstrate that substantial bias can also emerge from patterns of human geography. We show that in many states, Democrats are inefficiently concentrated in large cities and smaller industrial agglomerations such that they can expect to win fewer than 50 percent of the seats when they win 50 percent of the votes. To measure this "unintentional gerrymandering," we use automated districting simulations based on precinct-level 2000 presidential election results in several states. Our results illustrate a strong relationship between the geographic concentration of Democratic voters and electoral bias favoring Republicans.
An enduring fact of life in democratic electoral systems is that the party winning the largest share of the votes almost always receives a still larger share of the seats. This paper tests three models describing the inflation of the legislative power of the victorious party and then develops explanations of the observed differences in the swing ratio and the partisan bias of an electoral system. The “cube law” is rejected as a description, since it assumes uniformity (which is not observed in the data) across electoral systems. Explanations for differences in swing ratio and bias are found in variations in turnout over districts, the extent of the “nationalization” of politics, and, most importantly, in who does the districting or reapportionment. The measures of swing ratio and partisan bias appear useful for the judicial evaluation of redistricting schemes and may contribute to the reduction of partisan and incumbent gerrymandering.
Citizen demands for more accountability and transparency are implicitly grounded in a model of political representation based primarily on sanctions, in which the interests of the representative (in economic terms, the agent) are presumed to conflict with those of the constituent (in economic terms, the principal). A selection model of political representation, as with a selection model of principal-agent relations more generally, is possible when the principal and agent have similar objectives and the agent is already internally motivated to pursue those objectives. If a potential representative’s intrinsic goals (overall direction and specific policies) are those the constituent desires and if the representative also has a verifiable reputation of being both competent and honest, a constituent can select that representative for office and subsequently spend relatively little effort on monitoring and sanctioning. The higher the probability that the objectives of principal and agent may be aligned, the more efficient it is for the principal to invest resources ex ante, in selecting the required type, rather than ex post, in monitoring and sanctioning. A selection model is efficient when agents face unpredictable future decisions, are hard to monitor, and must act flexibly. Accountability through monitoring and sanctioning is appropriate to the sanctions model, narrative accountability and deliberative accountability to the selection model. Normatively, the selection model tends to focus the attention of both citizens and representatives on the common interest. In political science the selection model was advanced in the early 1960s as one of the two paths to constituency control, but after the 1970s was eclipsed by the sanctions model in spite of data seeming to indicate that in many circumstances it has greater predictive power. Economists have only recently begun to apply the selection model significantly to politics.
Assessing the Current North Carolina Congressional Districting Plan: Amended Report
- Simon Jackman