Legislative Redistricting

The definition of partisan symmetry as a standard for fairness in redistricting; methods and software for measuring partisan bias and electoral responsiveness; discussion of U.S. Supreme Court rulings about this work. Evidence that U.S. redistricting reduces bias and increases responsiveness, and that the electoral college is fair; applications to legislatures, primaries, and multiparty systems.

U.S. Legislatures

How to Measure Legislative District Compactness If You Only Know it When You See it
Aaron Kaufman, Gary King, and Mayya Komisarchik. Working Paper. “How to Measure Legislative District Compactness If You Only Know it When You See it”.Abstract
The US Supreme Court, many state constitutions, and numerous judicial opinions require that legislative districts be "compact," a concept assumed so simple that the only definition given in the law is "you know it when you see it." Academics, in contrast, have concluded that the concept is so complex that it has multiple theoretical dimensions requiring large numbers of conflicting empirical measures. We hypothesize that both are correct -- that the concept is complex and multidimensional, but one particular unidimensional ordering represents a common understanding of compactness in the law and across people. We develop a survey method designed to elicit this understanding with high levels of intracoder and intercoder reliability (even though the standard paired comparison approach fails). We then create a statistical model that predicts, with high accuracy and solely from the geometric features of the district, compactness evaluations by judges and other public officials from many jurisdictions, as well as redistricting consultants and expert witnesses, law professors, law students, graduate students, undergraduates, ordinary citizens, and Mechanical Turk workers. As a companion to this paper, we offer data on compactness from our validated measure for 18,215 US state legislative and congressional districts, as well as software to compute this measure from any district shape. We also discuss what may be the wider applicability of our general methodological approach to measuring important concepts that you only know when you see.
The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after LULAC v. Perry
The U.S. Supreme Court responds favorably to the nonpartisan Amici Curae Brief on partisan gerrymandering filed by Gary King, Bernard Grofman, Andrew Gelman, and Jonathan Katz (see brief) and requests additional information. This information is provided in the context of a brief history of the scholarly literature, a summary of the state of the art in conceptualization and measurement of partisan symmetry, and the state of current jurisprudence, in: Bernard Grofman and Gary King. 2008. “The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after LULAC v. Perry.” Election Law Journal, 6, 1, Pp. 2-35.Abstract

While the Supreme Court in Bandemer v. Davis found partisan gerrymandering to be justiciable, no challenged redistricting plan in the subsequent 20 years has been held unconstitutional on partisan grounds. Then, in Vieth v. Jubilerer, five justices concluded that some standard might be adopted in a future case, if a manageable rule could be found. When gerrymandering next came before the Court, in LULAC v. Perry, we along with our colleagues filed an Amicus Brief (King et al., 2005), proposing the test be based in part on the partisan symmetry standard. Although the issue was not resolved, our proposal was discussed and positively evaluated in three of the opinions, including the plurality judgment, and for the first time for any proposal the Court gave a clear indication that a future legal test for partisan gerrymandering will likely include partisan symmetry. A majority of Justices now appear to endorse the view that the measurement of partisan symmetry may be used in partisan gerrymandering claims as “a helpful (though certainly not talismanic) tool” (Justice Stevens, joined by Justice Breyer), provided one recognizes that “asymmetry alone is not a reliable measure of unconstitutional partisanship” and possibly that the standard would be applied only after at least one election has been held under the redistricting plan at issue (Justice Kennedy, joined by Justices Souter and Ginsburg). We use this essay to respond to the request of Justices Souter and Ginsburg that “further attention … be devoted to the administrability of such a criterion at all levels of redistricting and its review.” Building on our previous scholarly work, our Amicus Brief, the observations of these five Justices, and a supporting consensus in the academic literature, we offer here a social science perspective on the conceptualization and measurement of partisan gerrymandering and the development of relevant legal rules based on what is effectively the Supreme Court’s open invitation to lower courts to revisit these issues in the light of LULAC v. Perry.

Hidden Section

The concept of partisan symmetry

The concept of partisan symmetry as a standard for assessing partisan gerrymandering:
Democratic Representation and Partisan Bias in Congressional Elections
Defines, distinguishes, and measures "partisan bias" and "electoral responsiveness" (or "repesentation"), key concepts that had been conflated in much previous academic literature, and "partisan symmetry" as the definition of fairness to parties in districting. A consensus in the academic literature on partisan symmetry as the definition of partisan fairness has held since this article. Gary King and Robert X Browning. 1987. “Democratic Representation and Partisan Bias in Congressional Elections.” American Political Science Review, 81, Pp. 1252–1273.Abstract
The translation of citizen votes into legislative seats is of central importance in democratic electoral systems. It has been a longstanding concern among scholars in political science and in numerous other disciplines. Through this literature, two fundamental tenets of democratic theory, partisan bias and democratic representation, have often been confused. We develop a general statistical model of the relationship between votes and seats and separate these two important concepts theoretically and empirically. In so doing, we also solve several methodological problems with the study of seats, votes and the cube law. An application to U.S. congressional districts provides estimates of bias and representation for each state and deomonstrates the model’s utility. Results of this application show distinct types of representation coexisting in U.S. states. Although most states have small partisan biases, there are some with a substantial degree of bias.
Seats, Votes, and Gerrymandering: Measuring Bias and Representation in Legislative Redistricting
Robert X Browning and Gary King. 1987. “Seats, Votes, and Gerrymandering: Measuring Bias and Representation in Legislative Redistricting.” Law and Policy, 9, Pp. 305–322.Abstract
The Davis v. Bandemer case focused much attention on the problem of using statistical evidence to demonstrate the existence of political gerrymandering. In this paper, we evaluate the uses and limitations of measures of the seat-votes relationship in the Bandemer case. We outline a statistical method we have developed that can be used to estimate bias and the form of representation in legislative redistricting. We apply this method to Indiana State House and Senate elections for the period 1972 to 1984 and demonstrate a maximum bias 6.2% toward the Republicans in the House and a 2.8% bias in the Senate.
Racial Fairness in Legislative Redistricting
Related work on clarifying normative assumptions underlying proposed standards for fairness to different ethnic groups, and formalizes several absolute standards. Gary King, John Bruce, and Andrew Gelman. 1996. “Racial Fairness in Legislative Redistricting.” In Classifying by Race, edited by Paul E Peterson, Pp. 85-110. Princeton: Princeton University Press.Abstract
In this chapter, we study standards of racial fairness in legislative redistricting- a field that has been the subject of considerable legislation, jurisprudence, and advocacy, but very little serious academic scholarship. We attempt to elucidate how basic concepts about "color-blind" societies, and similar normative preferences, can generate specific practical standards for racial fairness in representation and redistricting. We also provide the normative and theoretical foundations on which concepts such as proportional representation rest, in order to give existing preferences of many in the literature a firmer analytical foundation.

Methods for measuring partisan bias and electoral responsiveness

The methods for measuring partisan bias and electoral responsiveness, and related quantities, that first relaxed the assumptions of exact uniform partisan swing and the exact correspondence between statewide electoral results and legislative electoral results, among other improvements:
Representation Through Legislative Redistricting: A Stochastic Model
The first attempt to eliminate the exact uniform partisan swing assumption, using data from a single election. Gary King. 1989. “Representation Through Legislative Redistricting: A Stochastic Model.” American Journal of Political Science, 33, Pp. 787–824.Abstract
This paper builds a stochastic model of the processes that give rise to observed patterns of representation and bias in congressional and state legislative elections. The analysis demonstrates that partisan swing and incumbency voting, concepts from the congressional elections literature, have determinate effects on representation and bias, concepts from the redistricting literature. The model shows precisely how incumbency and increased variability of partisan swing reduce the responsiveness of the electoral system and how partisan swing affects whether the system is biased toward one party or the other. Incumbency, and other causes of unresponsive representation, also reduce the effect of partisan swing on current levels of partisan bias. By relaxing the restrictive portions of the widely applied "uniform partisan swing" assumption, the theoretical analysis leads directly to an empirical model enabling one more reliably to estimate responsiveness and bias from a single year of electoral data. Applying this to data from seven elections in each of six states, the paper demonstrates that redistricting has effects in predicted directions in the short run: partisan gerrymandering biases the system in favor of the party in control and, by freeing up seats held by opposition party incumbents, increases the system’s responsiveness. Bipartisan-controlled redistricting appears to reduce bias somewhat and dramatically to reduce responsiveness. Nonpartisan redistricting processes substantially increase responsiveness but do not have as clear an effect on bias. However, after only two elections, prima facie evidence for redistricting effects evaporate in most states. Finally, across every state and type of redistricting process, responsiveness declined significantly over the course of the decade. This is clear evidence that the phenomenon of "vanishing marginals," recognized first in the U.S. Congress literature, also applies to these different types of state legislative assemblies. It also strongly suggests that redistricting could not account for this pattern.
Estimating the Electoral Consequences of Legislative Redistricting
The most technically sophisticated method, many aspects of which were simplified in the above paper. Andrew Gelman and Gary King. 1990. “Estimating the Electoral Consequences of Legislative Redistricting.” Journal of the American Statistical Association, 85, Pp. 274–282.Abstract
We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan bias and responsiveness along with measures of their variabilities from only a single year of electoral data. This allows one to distinguish systematic changes in the underlying electoral system from typical election-to-election variability.
A Unified Method of Evaluating Electoral Systems and Redistricting Plans
A now widely used set of methods for estimating bias and responsiveness, including applications to redistricting in the states and the U.S. Congress. Andrew Gelman and Gary King. 1994. “A Unified Method of Evaluating Electoral Systems and Redistricting Plans.” American Journal of Political Science, 38, Pp. 514–554.Abstract
We derive a unified statistical method with which one can produce substantially improved definitions and estimates of almost any feature of two-party electoral systems that can be defined based on district vote shares. Our single method enables one to calculate more efficient estimates, with more trustworthy assessments of their uncertainty, than each of the separate multifarious existing measures of partisan bias, electoral responsiveness, seats-votes curves, expected or predicted vote in each district in a legislature, the probability that a given party will win the seat in each district, the proportion of incumbents or others who will lose their seats, the proportion of women or minority candidates to be elected, the incumbency advantage and other causal effects, the likely effects on the electoral system and district votes of proposed electoral reforms, such as term limitations, campaign spending limits, and drawing majority-minority districts, and numerous others. To illustrate, we estimate the partisan bias and electoral responsiveness of the U.S. House of Representatives since 1900 and evaluate the fairness of competing redistricting plans for the 1992 Ohio state legislature.

Paradoxical benefits of redistricting

Demonstrates the paradoxical benefits of redistricting to American democracy, even partisan gerrymandering, (as compared to no redistricting) in reducing partian bias and increasing electoral responsiveness. (Of course, if the symmetry standard were imposed, redistricting by any means would produce less bias than any other arrangement.)
Enhancing Democracy Through Legislative Redistricting
Andrew Gelman and Gary King. 1994. “Enhancing Democracy Through Legislative Redistricting.” American Political Science Review, 88, Pp. 541–559.Abstract
We demonstrate the surprising benefits of legislative redistricting (including partisan gerrymandering) for American representative democracy. In so doing, our analysis resolves two long-standing controversies in American politics. First, whereas some scholars believe that redistricting reduces electoral responsiveness by protecting incumbents, others, that the relationship is spurious, we demonstrate that both sides are wrong: redistricting increases responsiveness. Second, while some researchers believe that gerrymandering dramatically increases partisan bias and others deny this effect, we show both sides are in a sense correct. Gerrymandering biases electoral systems in favor of the party that controls the redistricting as compared to what would have happened if the other party controlled it, but any type of redistricting reduces partisan bias as compared to an electoral system without redistricting. Incorrect conclusions in both literatures resulted from misjudging the enormous uncertainties present during redistricting periods, making simplified assumptions about the redistricters’ goals, and using inferior statistical methods.
Advantages of Conflictual Redistricting
A shortened, popular version of the previous article. Andrew Gelman, Gary King, Iain McLean, and David Butler. 1996. “Advantages of Conflictual Redistricting.” In Fixing the Boundary: Defining and Redefining Single-Member Electoral Districts, Pp. 207–218. Aldershot, England: Dartmouth Publishing Company.Abstract
This article describes the results of an analysis we did of state legislative elections in the United States, where each state is required to redraw the boundaries of its state legislative districts every ten years. In the United States, redistrictings are sometimes controlled by the Democrats, sometimes by the Republicans, and sometimes by bipartisan committees, but never by neutral boundary commissions. Our goal was to study the consequences of redistricting and at the conclusion of this article, we discuss how our findings might be relevant to British elections.

Other Districting Systems

Measuring the Consequences of Delegate Selection Rules in Presidential Nominations
Formalizes normative criteria used to judge presidential selection contests by modeling the translation of citizen votes in primaries and caucuses into delegates to the national party conventions and reveals the patterns of biases and responsiveness in the Democratic and Republican nomination systems. Stephen Ansolabehere and Gary King. 1990. “Measuring the Consequences of Delegate Selection Rules in Presidential Nominations.” Journal of Politics, 52, Pp. 609–621.Abstract
In this paper, we formalize existing normative criteria used to judge presidential selection contests by modeling the translation of citizen votes in primaries and caucuses into delegates to the national party conventions. We use a statistical model that enables us to separate the form of electoral responsiveness in presidential selection systems, as well as the degree of bias toward each of the candidates. We find that (1) the Republican nomination system is more responsive to changes in citizen votes than the Democratic system and (2) non-PR primaries are always more responsive than PR primaries and (3) surprisingly, caucuses are more proportional than even primaries held under PR rules and (4) significant bias in favor of a candidate was a good prediction of the winner of the nomination contest. We also (5) evaluate the claims of Ronald Reagan in 1976 and Jesse Jackson in 1988 that the selection systems were substantially biased against their candidates. We find no evidence to support Reagan’s claim, but substantial evidence that Jackson was correct.
Electoral Responsiveness and Partisan Bias in Multiparty Democracies
Unifies existing multi-year seats-votes models as special cases of a new general model, and was the first formalization of, and method for estimating, electoral responsiveness and partisan bias in electoral systems with any number of political parties. Gary King. 1990. “Electoral Responsiveness and Partisan Bias in Multiparty Democracies.” Legislative Studies Quarterly, XV, Pp. 159–181.Abstract
Because the goals of local and national representation are inherently incompatible, there is an uncertain relationship between aggregates of citizen votes and the national allocation of legislative seats in almost all democracies. In particular electoral systems, this uncertainty leads to diverse configurations of electoral responsiveness and partisian bias, two fundamental concepts in empirical democratic theory. This paper unifies virtually all existing multiyear seats-votes models as special cases of a new general model. It also permits the first formalization of, and reliable method for empirically estimating, electoral responsiveness and partisian bias in electoral systems with any number of political parties. I apply this model to data from nine democratic countries, revealing clear patterns in responsiveness and bias across different types of electoral rules.
Empirically Evaluating the Electoral College
Evaluates the partisan bias of the electoral college, and shows that there is little basis for reform of the system. Changing to popular vote of the president would not even increase individual voting power. Andrew Gelman, Jonathan Katz, and Gary King. 2004. “Empirically Evaluating the Electoral College.” In Rethinking the Vote: The Politics and Prospects of American Electoral Reform, edited by Ann N Crigler, Marion R Just, and Edward J McCaffery, Pp. 75-88. New York: Oxford University Press.Abstract

The 2000 U.S. presidential election rekindled interest in possible electoral reform. While most of the popular and academic accounts focused on balloting irregularities in Florida, such as the now infamous "butterfly" ballot and mishandled absentee ballots, some also noted that this election marked only the fourth time in history that the candidate with a plurality of the popular vote did not also win the Electoral College. This "anti-democratic" outcome has fueled desire for reform or even outright elimination of the electoral college. We show that after appropriate statistical analysis of the available historical electoral data, there is little basis to argue for reforming the Electoral College. We first show that while the Electoral College may once have been biased against the Democrats, the current distribution of voters advantages neither party. Further, the electoral vote will differ from the popular vote only when the average vote shares of the two major candidates are extremely close to 50 percent. As for individual voting power, we show that while there has been much temporal variation in relative voting power over the last several decades, the voting power of individual citizens would not likely increase under a popular vote system of electing the president.


JudgeIt II: A Program for Evaluating Electoral Systems and Redistricting Plans
Andrew Gelman, Gary King, and Andrew Thomas. 2010. “JudgeIt II: A Program for Evaluating Electoral Systems and Redistricting Plans”. Publisher's VersionAbstract
A program for analyzing most any feature of district-level legislative elections data, including prediction, evaluating redistricting plans, estimating counterfactual hypotheses (such as what would happen if a term-limitation amendment were imposed). This implements statistical procedures described in a series of journal articles and has been used during redistricting in many states by judges, partisans, governments, private citizens, and many others. The earlier version was winner of the APSA Research Software Award.