James Allison
Professor Emeritus, Psychology, Indiana University-Bloomington

In his majority opinion about partisan gerrymandering Chief Justice Roberts quoted a previous Court ruling, now the law of the land, that “one man’s vote in a congressional election is to be worth as much as another’s.” So the worth of a person’s vote must not depend on party affiliation, as it does under a partisan gerrymander. Nevertheless, Roberts declares that the Supreme Court shall give state legislatures free rein in setting up partisan gerrymanders, but not because the Court sanctions them. Not at all. The reason is that it’s just too hard to specify a judicial standard that courts could apply easily, uniformly, and universally in the task of recognizing a partisan gerrymander when they see one. Moreover, some gerrymanders will simply be too small to matter, and it’s hard to say how big is too big. And by the way, plaintiffs should just stop harping about proportional representation, this fantastic notion that if your party wins a certain proportion of the statewide vote it is entitled to the same proportion of the state’s congressional delegation. Why? Simply because the Constitution says nothing at all about proportional representation. And there’s no way you can derive proportional representation from the idea that all votes have equal worth. These notions form the core of Roberts’ ruling, and the following observations challenge them all.

Suppose we measure the representational worth of a vote in terms of the number of congressional seats won per vote—analogous to the gasoline worth of a dollar in terms of gallons per dollar. Concerning an election, we can then express the equal worth principle as (S_x/V_x) = (S_y/V_y), where S_x and S_y are the number of seats won by the respective parties, and V_x and V_y are the popular votes cast for the respective parties. In plain English, the equation says that the representational value of a vote is the same for both parties. One person’s vote in this congressional election was worth as much as another’s. But in a gerrymandered election, (S_x/V_x) > (S_y/V_y). The inequality says that in this congressional election a vote for Party X was worth more than a vote for Party Y.

Given the results of an actual election, these terms are not hard to calculate. In a state with multiple seats, for each race and each party we divide the number of seats won by the number of votes cast. In our winner take all system, the losing party gets zero seats per vote, and the winning party gets 1/N seats per vote, where N is the number of votes cast for that party. The end result would be two distributions of these numbers, one for each party. The question then is whether the two distributions differ significantly. The objective scientific answer would be provided by means of inferential statistics and their conventional decision rules, as validated by long use in the scientific community. A statistically significant difference would flag gerrymandered district maps in need of correction. Without such a difference, those maps would stand as drawn. This is one sure path toward an objective judicial standard readily accessible to all courts. In my home state of Indiana, such analyses applied to the 2018 election returns revealed statistically significant partisan gerrymandering in the races for Congress and for both houses of the state legislature.

And what if the difference is not statistically significant? There we reap a fine bonus: The lack of a significant difference would signify both the absence of any partisan gerrymander worth correction, and a close approach to proportional representation. The reason is simple: The equation that expresses the equal worth principle, when rearranged, expresses none other than proportional representation: ( S_x/ S_y) = (V_x/V_y). That is, the number of seats won is strictly proportional to the number of votes won. For example, a party with 50% more votes would win 50% more seats.

Thus, the tried and true constitutional principle of equal worth among votes can provide a practicable judicial standard for the detection of a partisan gerrymander. And at long last that very same principle reveals proportional representation as a legitimate object of constitutional protection, co-equal in every sense.

Plaintiffs, keep harping about proportional representation in your constitutional arguments against partisan gerrymanders. You have every right to do so.