Voting Rights, Mathematical Expertise, and the Limits of Legal Liberalism

Reuel Schiller

Can you imagine a better-timed piece of legal history than Alma Steingart’s insightful One Person, One Vote? The Gap between Representative Equity and Mathematical Equality after Baker v. Carr”? Published in the March 2026 issue of the Journal of American History, the article landed amidst a frenetic tit for tat of partisan and racial gerrymandering. In August 2025, President Trump demanded that Texas redraw its congressional districts to help keep a Republican majority in the House of Representatives in anticipation of Democratic successes in the 2026 midterms. Republican-dominated legislatures in Missouri, Ohio, and North Carolina followed suit, only to have California and Virginia respond with pro-Democratic gerrymanders, the last of these occurring just weeks after Steingart’s article appeared. Then, the courts got busy. Virginia’s Supreme Court overturned that state’s redistricting, and, most significantly, at the end of April 2026, the United States Supreme Court decided Louisiana v. Callais, eviscerating section 2 of the Voting Rights Act. This set off another burst of redistricting as Republican-controlled state legislatures carved up Democratic-leaning majority-minority districts to further boost their party’s chances in November.

Professor Steingart’s article can’t tell us how to end this grotesque carnival of democratic back-sliding, but it does a fantastic job of explaining how we got here. At the same time, it complicates the conventional narrative of the Warren Court’s landmark malapportionment cases. I’m sure that Jotwell’s readers are familiar with the fight over the justiciability of malapportionment claims in Baker v. Carr (1962) and the emergence of the “one person, one vote” standard that required legislative districts to contain roughly equal populations in Reynolds v. Sims (1964). These cases are often portrayed as the apex of legal liberalism. Earl Warren famously identified them as the Court’s greatest accomplishment during his time as Chief Justice. In the conventional narrative, which focused on the Court’s commitment to political equality and participatory democracy, they were emblematic of legal liberalism’s aspirations for an inclusive, egalitarian society. Steingart shows, however, that this account misses a crucial attribute of these cases. Their most significant legacy, Steingart argues, is that they set the parameters of the debate “about the meaning of representation in a distinctly mathematical idiom” that remains with us today. (P. 703.) Cases that seemed to be about political inclusion turned out to be ones that elevated mathematical reasoning over the facilitation of genuine political participation.

Steingart demonstrates this by focusing our attention away from the best-known opinions in Baker, Justice Brennan’s majority opinion and Justice Frankfurter’s dissent. Instead, she suggests that the foundational opinions for the voting rights cases that would emerge from Baker were Justice Clark’s concurrence and Justice Harlan’s dissent. Clark, “equat[ing] mathematics with rationality,” created a formula to calculate each voting district’s “total representation” and determined that the state’s apportionment plan failed the rational basis test required by the equal protection clause. (P. 708.) Harlan, on the other hand, rejected Clark’s “’facile mathematical argument.’” (P. 709.) He demonstrated how malleable mathematical approaches could be, and suggested that mathematical reasoning could not encompass the full range of values that might inform legitimate apportionment decisions. When, two years after Baker, the Court refined its malapportionment doctrine in Reynolds, it seemed to endorse a mathematical approach.  The principle of “one person, one vote” was designed to ensure that districts would be of the same size so that voters’ votes were weighed equally. Under this principle, the Court asserted, determining the constitutionality of an apportionment plan was “‘easily demonstrable mathematically.’” (P. 711.) The proper use of mathematical reasoning would lead to objectively fair, equitable districts.

Reynolds, as it turned out, did not immediately guarantee the primacy of mathematical evidence in voting rights cases. After her discussion of Baker and Reynolds, Steingart takes her readers through several voting rights cases involving weighted voting, multimember districts, and allegations of racial vote dilution. In each of these cases, she demonstrates that litigants and judges debated the utility of quantitative evidence in voting rights cases: Did statistical models improperly displace other values that should be part of districting decisions? If mathematical analysis was used in these cases, should it be used to determine only formal disparities in representation (is my vote equal to that of a voter in a neighboring district) or whether a person’s vote is actually effective (does a districting plan allow voters to “elect legislators of their choice,” particularly in instances where districts diluted the votes of racial minorities)? (P. 722.)

By the early 1970s, however, the “mathematical arms race” was on. (P.723.)  As voting rights cases came to turn increasingly on the effectiveness of a given vote, proof became more mathematically and statistically complicated. The increasing power of computers only furthered this trend. Courts continued to insist on districts of similar sizes, but increasingly sophisticated technology, statistical methods, and mathematical theories allowed for drawing districts with such numerical, demographic, and partisan detail that, ironically, the ultimate result of the introduction of mathematical techniques into the voting rights jurisprudence was to facilitate the types of precision gerrymandering that currently bedevil us.

This dismaying point is not, however, Steingart’s main analytic move. Instead, she makes a deeper argument about the relationship between math, politics, and law. Advocates and judges often reached for mathematical solutions in voting cases as an attempt to give objective content to the idea of equality. Yet, Steingart convincingly demonstrates that, in the realm of public policy, math and politics are inseparable — “the political and the mathematical are mutually constitutive.” (P. 705.) She makes this argument so convincingly because she is a gifted translator of mathematical concepts into language that can be easily understood, even by people whose mathematical training ended disastrously in freshman-year calculus.¹ She shows us exactly how mathematical arguments were used or rejected. She then demonstrates how different uses of mathematics determined outcomes in different cases, and ultimately defined the parameters of legal regulation in this crucial area of public policy. Because of its veneer of objectivity, mathematical analysis slipped back and forth between its use “as a descriptive tool and its use as a normative tool.” (P. 725.) In doing so, it shaped voting rights law in a manner that obscured, or at least rationalized, its policy content. Math gives us definitions of equality that seem sound, but are less than fair when implemented in the real world.

Steingart also has a lesson for intellectual historians of postwar America. She shows why discussions of the intellectual history of this period should include an examination of developments in mathematical, scientific, and technological thinking.  Some scholars, such as Fred Turner, have started down this path,² but Steingart’s granular description of the way mathematical reasoning impacted law and politics is pathbreaking.  It intersects with some of the pervasive themes that other historians have examined – the rise of participatory democracy and the increasing suspicion of expertise during the 1960s, for example. However, it does so in a manner that raises fascinating questions about the existing literature. The cases she describes illustrate battles over the use of expert, technical knowledge. Yet the forms of expertise she discusses – math and technology – are often ignored by intellectual historians. They also seem to have had more resilience in the face of rising suspicion of experts than many other domains of knowledge. Steingart’s article suggests that it would be worth exploring the sources of this resilience.

All of these themes – the unintended consequences of mathematical reasoning in voting rights cases, the hidden intermixing of policy and technology in these cases, and the curious resistance of mathematical expertise to critique — are vividly illustrated in the Supreme Court’s latest voting rights decision, Louisiana v. Callais.³ Justice Alito’s opinion uses technology to set up a de facto evidentiary standard for proving that a redistricting plan discriminates based on race. A voting rights plaintiff must “disentangle” impermissible racial gerrymandering from permissible political gerrymandering.⁴ In a world where districts are “produced by computer, as is generally the case today,” racial discrimination must be proven algorithmically.⁵ The state generates maps based on an algorithm containing its preferred districting criteria. The plaintiff must then prove discrimination by generating a map that satisfies all the same criteria but also creates a majority-minority district. Although Alito does not say it explicitly, this technological method of proof is now essentially the only way to prove a violation of the Voting Rights Act. After all, voting rights “litigants almost always have the wherewithal to proffer such a map if there is one to be found.”⁶

The Court has thus once again used a technique that Steingart so compellingly demonstrates is baked into the DNA of American voting rights jurisprudence. Proof by math and technology eclipses the reality of how voting works. Gone is a discussion of racial bloc voting. Gone is any mention of why partisan gerrymanders sit on a foundation of racial discrimination. Gone is any inquiry into the actual intent of legislators whose claim that they redrew districts for partisan reasons may be indistinguishable from racial animus absent non-algorithmic methods of proof. The criteria we use to draw voting districts reflect, and have always reflected, policy preferences. What Steingart’s fantastic article shows us is that, too often, these preferences have been hidden by a curtain of false mathematical and technological objectivity. While the Court has not learned this lesson (or willfully refuses to acknowledge it), Steingart’s scholarship pulls down this curtain. We can only hope that her work will allow for a candid acknowledgement of the political impact of math and technology as we eventually reconstruct this area of law and policy in a manner that promotes and protects a fully functional democratic system of government.

1. No, I don’t have any idea why this particular illustration came to mind.
2. Fred Turner, From Counterculture to Cyberculture: Stewart Brand, the Whole Earth Network, and the Rise of Digital Utopianism (2008).
3. 608 U.S. ____ (2026), slip opinion.
4. Id., at 34.
5. Id., at 21.
6. Id., at 25.