The Measure of a Metric: The Debate over Quantifying Partisan Gerrymandering.

• Author: Stephanopoulos, Nicholas O.

Abstract. Over the last few years, there has been an unprecedented outpouring of scholarship on partisan gerrymandering. Much of this work has sought either to introduce new measures of gerrymandering or to analyze a metric--the efficiency gap--that we previously developed. In this Essay, we reframe the debate by presenting a series of criteria that can be used to evaluate gerrymandering metrics: (1) consistency with the efficiency principle; (2) distinctness from other electoral values; (3) breadth of scope; and (4) correspondence with U.S. electoral history. We then apply these criteria to both the efficiency gap and other measures. The efficiency gap complies with our criteria under all circumstances. Other metrics, in contrast, often violate the efficiency principle and cannot be used in certain electoral settings.

Introduction I. Evaluative Criteria A. Efficiency B. Distinctness C. Scope D. Correspondence II. Evaluating the Efficiency Gap A. Efficiency B. Distinctness C. Scope D. Correspondence III. Critiques of the Efficiency Gap A. Methodology B. Variability C. Ideology IV. Other Gerrymandering Metrics A. Multiplicity B. Relationships C. Reservations Conclusion Appendix A Introduction

For several decades, there was "virtually a consensus [in] the scholarly community" about how to measure partisan gerrymandering. (1) An analyst would estimate the seat shares the major parties would win in a state if (hypothetically) they each received the same vote share. The greater the divergence between the parties' seat shares for the same (counterfactual) vote share, the larger a district plan's partisan bias, and the more gerrymandered the plan. (2)

Despite the metric's wide acceptance among academics, the U.S. Supreme Court's pivotal member, Justice Kennedy, has expressed misgivings about partisan bias. In a 2006 case, he did not "altogether discount[] its utility in redistricting planning and litigation," but he did worry that "[t]he existence or degree of [bias] may in large part depend on conjecture about where possible vote-switchers will reside." (3) He noted: "[W]e are wary of adopting a constitutional standard that invalidates a map based on unfair results that would occur in a hypothetical state of affairs." (4)

The two of us agree with Justice Kennedy that it is odd to measure partisan gerrymandering based on how the major parties would have performed in counterfactual elections. It is more intuitive, in our view, to assess gerrymandering based on how the parties did perform in elections that in fact took place. That is why, a few years ago, we sought to unsettle the scholarly consensus in favor of partisan bias by introducing a new metric--the efficiency gap--that does not rely on predictions about what would occur in hypothetical electoral scenarios. (5)

The efficiency gap is rooted in the insight that partisan gerrymandering is always carried out in one of two ways: the cracking of a party's supporters across many districts, in which their preferred candidates lose by relatively narrow margins, or the packing of a party's backers into a few districts, in which their preferred candidates win by overwhelming margins. (6) Both cracking and packing produce what are known as wasted votes--votes that do not contribute to a candidate's election. In the case of cracking, all votes cast for the losing candidate are wasted; in the case of packing, votes cast for the winning candidate above the 50% (plus one) threshold needed for victory are wasted. The efficiency gap is simply one party's total wasted votes in an election, minus the other party's total wasted votes, divided by the total number of votes cast. It captures in a single figure the extent to which district lines crack and pack one party's voters more than the other's. (7)

It is fair to say that since we introduced the efficiency gap, there has been an explosion of judicial and academic interest in the measurement of partisan gerrymandering. In the courts, one of us has helped to litigate a pair of lawsuits based in part on the efficiency gap--one a challenge to Wisconsin's state house plan; (8) the other, to North Carolina's congressional map. (9) The three-judge district court in the Wisconsin case struck down the plan on partisan gerrymandering grounds in November 2016--the first such victory in more than thirty years--and the state's appeal is currently pending before the Supreme Court. (10) In the North Carolina case, the three-judge district court also invalidated the map in January 2018. (11)

In the academy, scholars have developed several new measures of partisan gerrymandering and have commented extensively on the efficiency gap. One of these new metrics is the mean-median difference: the difference between a party's mean vote share and its median vote share across all the districts in a plan. When a party's median vote share is lower than its mean vote share, the party is arguably the victim of gerrymandering. (12) Another new metric is the difference between the parties' average margins of victory. If one party's wins are more lopsided than the other party's, this may indicate that its supporters have been cracked and packed by the district lines. (13) Scholars have also proposed variants of both partisan bias (by averaging it across all electoral outcomes rather than for a single hypothetical election) (14) and the efficiency gap (by varying the definitions and weights of the two types of wasted votes). (15)

The academic discussion of the efficiency gap includes a number of criticisms of the measure. Writing in this journal's pages, Benjamin Cover contends that the efficiency gap is in tension with important democratic values. In his view, it favors uncompetitive elections, discourages proportional representation, and incentivizes voter suppression. (16) Cover and John Nagle also object to some of the methodological choices underpinning the efficiency gap: how wasted votes are defined and weighted, how imputations are made for uncontested races, and how variations in district-level turnout are addressed. (17) Wendy Tam Cho, Robin Best and colleagues, and Jonathan Krasno and colleagues further complain about the metrics variability from election to election. (18) These scholars present both toy examples of one or two districts and actual district plans that they argue demonstrate this variability. (19) And Christopher Chambers and colleagues observe that the efficiency gap does not distinguish between moderate and extreme legislators. This oversight may allegedly lead to odd conclusions about certain maps. (20)

We find these criticisms unpersuasive, and we explain why later in this Essay. We are also skeptical of the measures other scholars have recently advanced. But before diving into these metrics' pros and cons, we think it is worthwhile to step back and ask what it is we want from a quantitative measure of partisan gerrymandering. What properties would such a metric ideally exhibit?

One attribute is consistency with what one of us has labeled the efficiency principle. This is simply the idea that when a party's seat share increases while its vote share remains constant, a measure should reflect that party's growing advantage. (21) The essence of partisan gerrymandering is winning more seats without appealing to more voters, and a valid metric should capture that conceptual core.

A second feature is distinctness from other democratic values. District plans implicate not just partisan fairness but also electoral competitiveness, voter participation, legislative polarization, and so on. But it is only partisan unfairness that lies at the heart of partisan gerrymandering. Thus only such unfairness should be revealed by a gerrymandering measure.

A third criterion is breadth of scope. In other words, a metric should be usable under a range of electoral conditions: when the parties are evenly matched statewide or when one party predominates, when turnout is or is not roughly equal in each district, and when there are two or more than two parties competing for office. Without such flexibility, a measure would be inapplicable to many common scenarios.

And a fourth characteristic is empirical correspondence. That is, the electoral ideal implied by a metric should not be too different from the historical norm in the United States. Otherwise the measure would imply that most plans in the United States have been gerrymanders--and its adoption would be so disruptive as to be infeasible.

These criteria are why we endorse the efficiency gap. First, as suggested by its name, it is indeed consistent with the efficiency principle. When a party wins a larger (smaller) seat share for the same vote share, the metric always shifts in favor of (against) that party.

Second, the efficiency gap does not conflate partisan fairness with other democratic values. In particular, there is no connection between the measure and electoral competitiveness. Conceptually, any efficiency gap is compatible with any level of competitiveness because it is only the difference between the parties' average margins of victory that affects the metric. Empirically, too, U.S. elections have exhibited essentially a zero correlation between the efficiency gap and competitiveness over the last half-century.

Third, as recently generalized by one of us, the efficiency gap is usable in almost every electoral environment: competitive or uncompetitive, with or without equal district turnout, and whether two or more than two parties are running. (22) The measure's only limitation is one that applies equally to all gerrymandering metrics: namely, that they are prone to large values (and large swings) when the number of districts is small. (23)

And fourth, the efficiency gap corresponds closely to the empirical realities of U.S. elections. Over the last fifty years, congressional and state house plans have both had mean and median efficiency gaps near zero. As the parties' vote...