Gerrymandering 101

James Allison
Professor Emeritus, Psychology, Indiana University

What is a Gerrymander?

To make a proper gerrymander, draw the map of election districts so the votes of the group you favor are worth more per capita than those of the group you disfavor. Try to deflate the value of your opponent’s votes by packing as many as you can into the fewest possible districts. As a result, your favored group is likely to win more seats in the state legislature or the Congress than its share of the popular vote would warrant. A useful measure of the worth of one’s vote is S/V, the number of seats we get per vote. If your candidate wins, your share of that one seat is 1/N, where N is the number of us who voted for that candidate. If our candidate loses we get nothing, so each loser’s share is 0/N. By means of inferential statistics we can decide whether any group difference in S/V is statistically significant, and therefore the product of a gerrymandered election.

Specific Examples

In our typical racial gerrymander a white person’s vote is worth significantly more than a black person’s vote. In a partisan gerrymander a vote for one political party is worth significantly more than a vote for another political party. In the 2018 congressional elections, a North Carolina Republican’s vote was worth significantly more than a Democrat’s. In Maryland the opposite was true. In Indiana a Republican’s vote was worth significantly more than a Democrat’s in the races for Congress and for both houses of the state legislature. In Washington state’s congressional election there was no significant difference between the two major parties.


Federal courts at all levels have long acknowledged the constitutional principle that one person’s vote is worth the same as any other’s vote. This one person-one vote principle applies now, but did not always apply, to the poor, the black, the female, and persons as young as 18. We have a continuing legal and societal battle about who is eligible to vote. A frequent expression of that fact is that the Constitution does not guarantee the right to vote. Who then is covered by this constitutional guarantee of one person-one vote? Individual states have had considerable latitude in adjudicating this question. For example, various states have denied voting rights to prison inmates, convicted felons, and registered voters who happen to lack some arbitrary form of identification.

Implications for Gerrymander

The Supreme Court of the United States has ruled that racial gerrymanders are unconstitutional, but partisan gerrymanders are not. In a 5-4 decision rendered last month, the majority admitted that all gerrymanders violated the constitutional principle that one person’s vote is worth the same as any other’s. But the Court went on to conclude that partisan gerrymanders are local political creatures that the states, and not the federal Supreme Court, should adjudicate as they see fit.

The majority explained, as the Court had done before, that it simply lacked a judicial standard by which to identify a gerrymander uniformly among all possible venues. Moreover, plaintiffs should discard proportional representation as a constitutional argument against partisan gerrymandering, because the Constitution makes no mention of the notion that congressional representation should be proportional to the popular vote. Furthermore, there was no way to derive proportional representation from one person- one vote.

Finally, the majority said that if the citizens of a particular state became dissatisfied with the district maps produced by the state legislature, they could always reform the redistricting process themselves. In many states citizen-initiated referenda had created redistricting commissions with significant input from citizens independent of the state legislature.


Plaintiffs objected that many states have constitutions that forbid citizen initiatives, and legislatures disinclined to amend such constitutions. One plaintiff remarked that, contrary to former Justice Sandra Day O’Connor, who thought such inequities would gradually correct themselves, the situation had grown worse, not better, since her time on the Court. The problem is not self-correcting.

Contrary to Chief Justice Roberts, who wrote the majority opinion, it is not difficult to establish a workable judicial standard applicable to all venues. The seats/vote metric is one such standard, easily calculated from election returns and easily analyzed by means of inferential statistics widely used in the scientific community. Finally, the algebraic expression of equal seats/vote reveals one person-one vote and proportional representation as two sides of the same coin.* It follows that if the Constitution protects one person-one vote, it also protects proportional representation, contrary to Justice Roberts. Sooner or later, his deeply flawed opinion on partisan gerrymandering must fall.

What to Do

Get your state court to nullify your state’s district map for any partisan violation of the constitutional guarantees of one person-one vote and proportional representation. According to Roberts’ majority opinion, the Supreme Court has left partisan gerrymanders to the states, and should therefore refuse to hear an appeal from your state court’s ruling. But don’t count on it.

Jawbone your legislators to the point at which they decide to allow significant citizen representation, independent of the legislature, on the state’s redistricting commission.

*If S/V represents the number of seats won per vote, and d and r represent two political parties, the constitutional principle of one person-one vote implies that Sd/ Vd = Sr/ Vr: In plain English, a Democrat’s vote must have the same worth as a Republican’s vote. If we multiply both sides of that equation by Vr/ Sd, we get Vr/ Vd = Sr/Sd: In plain English, a party’s relative share of the seats it wins must equal its relative share of the popular vote. Thus, the Constitution protects both one person-one vote and proportional representation as two sides of the same coin, contrary to Justice Roberts’ majority opinion in Rucho v. Common Cause (18-422, June 27, 2019).