minority “communities of interest” have historically only been guaranteed representation through the practice of “racial gerrymandering,” a practice ruled unconstitutional in the recent US Supreme Court’s decision in Louisiana v. Callais.

the Massachusetts House delegation has been entirely Democratic for the past three decades, despite a significant Republican vote share due to the relatively uniform distribution of Republican voters in the state.

Unfortunately, the Supreme Court did not find this argument to be persuasive, ruling instead that the question of partisan gerrymandering is “nonjusticiable”—outside their jurisdiction. Subsequent rulings, such as Abbott v. League of United Latin American Citizens, give little hope that the Supreme Court will impede future gerrymandering.

A much better mathematical method to detect gerrymandering, known as Markov chain Monte Carlo (MCMC) sampling, has been percolating throughout the research literature, and was brought before the Supreme Court in the 2019 case Rucho v. Common Cause. Although it is not possible to compare a contested map against all possible maps, MCMC uses a computational technique called a “random walk” to generate a representative sample of legal electoral district maps by repeatedly making small arbitrary changes to possible district boundaries. Mathematicians, serving as expert witnesses for the plaintiffs and weighing in as amicus curie, argued that if a specific map is an outlier from the rest of samples in terms of political advantage, it indicates possible gerrymandering. The mathematicians found that maps proposed by the 2012 and 2016 North Carolina legislatures fell at the extreme ends of bell curves generated from MCMC-sampled maps, based on measures such as the number of Democrats elected and the number of Democratic voters in specific districts.

A redistricting plan proposed by Republican legislators in Wisconsin in 2011 was overturned by a lower court based in part on the magnitude of the efficiency gap, although this ruling was overturned in 2018 by the US Supreme Court in Gill v. Whitford. In oral arguments, Chief Justice John Roberts dismissed this metric as “sociological gobbledygook.” Roberts’ critique is unfair in substance because the efficiency gap is a mathematical formula, not nonsense. But it is not entirely wrong in spirit. Some mathematicians have argued that these metrics do not accurately reflect “common-sense understanding of political unfairness.”

How can we identify gerrymandered maps if not by sight? Numerical metrics such as the Polsby–Popper test attempt to measure the “compactness” of an electoral district (the ratio of its area to the square of its perimeter), while the efficiency gap calculates the number of “wasted” votes by computing the proportion of votes that are not used to elect a winner.

These techniques are traditionally thought to create weirdly shaped districts, such as the “praying mantis” district in Maryland, the “Goofy kicking Donald Duck” district in Pennsylvania, and the “earmuffs” district in Illinois. But some heavily gerrymandered maps, such as North Carolina’s, look normal to the naked eye.

However, Texas, California, Missouri, North Carolina, and Virginia have recently approved unusual mid-decade redistricting plans in advance of the upcoming US House of Representatives election in November 2026, approving new maps designed to advantage either the Democratic or Republican party. Pending decisions by courts, legislatures, and voters may potentially extend these practices to other states such as Louisiana and Florida.

What questions should stakeholders ask when evaluating proposed district maps or charting a course for future elections?

Mosca backs up histhesis with this assertion: It's the power of organization thatenables the minority always to rule. There are organizedminorities and they run things and men. There are unorganizedmajorities and they are run.

On examination, you will find this very judiciary oppressively constructed; your jury trial destroyed, and the judges dependent on Congress.

A bare majority in these four small states may hinder the adoption of amendments; so that we may fairly and justly conclude that one twentieth part of the American people may prevent the removal of the most grievous inconveniences and oppression, by refusing to accede to amendments. A trifling minority may reject the most salutary amendments. Is this an easy mode of securing the public liberty It is, sir, a most fearful situation, when the most contemptible minority can prevent the alteration of the most oppressive government; for it may, in many respects, prove to be such. Is this the spirit of republicanism?

Democrats won’t be able to use reconciliation to enact the government-reform bill that House Democrats adopted in 2019, which among other things would create two weeks of early voting in all 50 states and put redistricting in the hands of nonpartisan, independent commissions.

Here’s the grim kicker: The conditions that made Trump and this Republican Party possible are set to worsen. Republicans retained control of enough statehouses to drive the next redistricting effort, too, and their 6-3 majority on the Supreme Court will unleash their map-drawers more fully. The elections analyst G. Elliott Morris estimates that the gap between the popular vote margin and the tipping point-state in the Electoral College will be 4-5 percentage points, and that the GOP’s control of the redistricting process could push it to 6-7 points next time.

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The formula is simple: divide the population by the number of congressional or legislative districts and use the existing geo-political boundaries to come as close to the required number as possible.