Condorcet Voting and the Cornyn-Paxton Race

The upcoming U.S. Senate election in Texas perfectly illustrates the importance of this voting reform.

The University of Chicago’s Center for Effective Government, as part of its “Democratic Reform Primer Series,” has published an introductory explanation of Condorcet Voting co-authored by Eric Maskin and me. I’m honored to continue my collaboration with Eric with this piece and to have it included in this valuable collection of papers.

To understand why publication of this explainer on Condorcet Voting is especially timely right now, look no further than the looming U.S. Senate race in Texas. The state’s attorney general, Ken Paxton, is challenging incumbent Senator John Cornyn in the Republican primary. Paxton is a deep red MAGA candidate, practically falling off the far-right end of the red-blue partisan spectrum. Cornyn is a traditionally conservative Republican, which in this Trump-dominated era makes him a RINO (“Republican In Name Only”) according to many Trump loyalists.

Polls consistently show Paxton with a large lead over Cornyn in the primary. As a consequence, Cornyn has been attempting to reposition himself as closer to Trump despite having distanced himself from Trump previously. Paxton proclaims himself to be a pure Trump loyalist. Trump, for now, has declined to make an endorsement.

Assuming that Trump fails to come to Cornyn’s rescue by endorsing him over Paxton (and assuming also that no third candidate enters the GOP primary, as might happen), Paxton is likely to win the Republican nomination. Polls show that the general election between Paxton and Colin Allred, the most likely Democratic nominee, would be close. But given that it’s Texas, which has remained reliably red despite the efforts of Democrats to turn it purple, Paxton probably would win in the end.

Cornyn, however, almost certainly would be the Condorcet Winner in a three-candidate race with Paxton and Allred. The polling shows Cornyn defeating Allred in the general election if Cornyn can make it through the GOP primary—and doing so more easily than Paxton would. Among all Texas voters, and not just Republican primary voters, Cornyn easily would defeat Paxton head-to-head as Democrats would join moderate independents and less extreme Republicans in endeavoring to defeat the ultra-extreme Paxton. Preferred by a majority of voters of each opponent would make Cornyn, by definition, a Condorcet Winner among these three candidates.

Thus, this Texas race is clearly one for which it makes a huge difference whether or not the election is conducted with Condorcet Voting. Without Condorcet Voting, the Senate is most likely to add another far-right MAGA member, rather than the more moderate conservative whom a majority of the state’s voters actually prefer. With Condorcet Voting, the winning candidate would be the one that a majority preferred to each alternative, and the Senate would be less polarized. Cornyn also would be less pressured to change himself into a Trump acolyte if Texas used Condorcet Voting for this election.

It is important to understand that only a Condorcet Voting system can achieve an outcome consistent with what a majority of the state’s voters most want—and avoid the polarized outcome of Paxton’s election that otherwise would occur. If Texas adopted the kind of “top two” system that California has, the top two candidates would be Paxton and the Democrat, even though Cornyn still would be the Condorcet Winner among the three. This point is the essential one that James Madison understood when he said in 1823 that it is necessary to have a runoff among the top three, not top two, candidates in order to elect “the real preference of the Voters” because it “not infrequently happens” that the third candidate in terms of first-choice votes is preferred by a majority when considered one-on-one against each of the top two.

For the same reason, using Alaska’s “top four” system with Instant Runoff Voting would fail to elect Cornyn as the “real preference of the Voters” and thus would not make a difference in the result compared to the existing electoral system. As long as Cornyn remains in third place in terms of first-choice votes, Instant Runoff Voting would eliminate him from contention and make the race come down to a choice between Paxton and the Democrat, just like California’s “top two” system. Accordingly, it’s essential to adopt a Condorcet Voting system in order to have the outcome of this 2026 U.S. Senate election in Texas conform to the will of the majority in the state—which is why this election is such an apt illustration of Condorcet Voting’s importance.

If you are previously unfamiliar with Condorcet Voting, the primer that Eric Maskin and I have written is a good a place to start in order to understand the basics of this key electoral concept.

I will also be discussing the history of Condorcet Voting and its continuing relevance in a lecture at the University of Melbourne next week. When a video of that lecture is available, I will post it.