It is often argued that the prevailing system of partisan primaries followed by a plurality-winner general election is a sensible way for an electorate to make a clear policy choice between one left-of-center option and one right-of-center alternative.

But one of Ohio’s primaries yesterday offers a clear counterexample to that argument. Featured in a New York Times story, the House seat at issue is Ohio’s Ninth Congressional District. The incumbent is a Democrat, Marcy Kaptur, who was unopposed in her party’s primary. In November she will face J.R. Majewski, who won the Republican primary with about 36% of the vote.

Majewski, according to the N.Y. Times description, is arguably even more extreme than Majorie Taylor Greene. If he wins, he would be one more vote for the “Big Lie” caucus. Looking ahead to January 6, 2025, if he were an incumbent House member then, would he vote to uphold valid electoral votes cast for Donald Trump’s Democratic opponent if Trump was asking his supporters in the House to nullify those electoral votes? Perhaps relevant to answering that question is this passage from the Times piece:

‘…he first gained attention in Ohio by turning his lawn into a 19,000-square-foot “Trump 2020” sign.

During his campaign, he ran one ad showing him carrying an assault-style rifle in which he says, “I’m willing to do whatever it takes to return this country back to its former glory,” adding, “If I’ve got to kick down doors, well, that’s just what patriots do.”‘

Of course, if he’s the candidate the voters of his district most want, then he’s the one who should be sent to the House to represent his district. But even if he wins the general election against Kaptur in November, is he really the candidate that the electorate of his district as a whole most want?

As the N.Y. Times story also observes, in achieving his 36% plurality win in the primary yesterday, Majewski ran ahead of “two lower-key Republicans for the nomination.” Craig Riedel came in second with about 31% of the vote. Theresa Gavarone was third with 29%.

We can’t be sure that Majewski would have won a runoff, or an “instant runoff” using ranked-choice voting, against Riedel. Thus, even though he’s now officially the nominee of the Republican party, we can’t really be sure he is actually the most preferred choice of the district’s GOP voters among the alternatives. His plurality win is not the same thing as being the candidate whom most GOP voters in the district would most prefer.

Indeed, it’s possible that Majewski would have been the “Condorcet loser” if ranked-choice ballots had been used in the GOP primary. A “Condorcet loser” is the single candidate in a multi-candidate field who would lose every one-on-one comparison with every other candidate in the race. In other words, when compared to each other candidate, a majority of voters prefer the Condorcet loser’s opponent. So, to put this point in the context of yesterday’s primary, it’s easily conceivable that a majority of yesterday’s GOP voters would have preferred Riedel to Majewski, and also a majority of yesterday’s GOP voters would have preferred Gavarone to Majewksi. And yet Majewski was declared the GOP nominee with his plurality.

Nor do we know that November voters would prefer Majewski to Riedel or Gavarone. Just because Majewski beats Kaptur, if that’s what happens in November, it doesn’t mean that Riedel or Gavarone wouldn’t have won by even higher margins. It just means that in November the district voters really don’t want a Democrat (as might happen if Democrats have a really bad midterm this year).

So the winner in the end could be a candidate who is the Condorcet loser of his own party’s primary and also the least preferred Republican among the district’s general election voters.

Is this a rational two-party system?