The city also will have its first openly gay mayor, in Mr. Leno, or its first black female mayor, in Ms. Breed. That may not be a coincidence; ranked-choice voting has led to greater diversity around the country, partly because higher-turnout elections tend to be more diverse. In votes for 53 seats in San Francisco and other Bay Area cities that have adopted ranked-choice, minority candidates have won 62 percent of the time, up from 38 percent in previous elections, according to FairVote, a group that advocates for electoral reforms.

It’s hard to argue against increased voter turnout or more civility and substance in political campaigns, but some people are still skeptical of ranked-choice voting, particularly candidates and parties who are used to an up-or-down, zero-sum system. The most common criticisms are that ranked-choice is too expensive to run and too hard for voters to understand. But ballots can be designed intuitively, as Maine’s are, and voters in places that use ranked-choice have had very few problems. In San Francisco last week, voters made eight times as many errors on ballots for the gubernatorial primary, which was run using the standard method, as they did on mayoral ballots, which used ranked-choice. As for the financial impact, ranked-choice voting may in fact end up costing taxpayers — and candidates — less by eliminating the need for expensive runoff elections, which also suffer from poor turnout.

In Maine, voters adopted ranked-choice in 2016 because independent candidates there often draw enough votes to prevent any candidate from winning a majority. However, the debate over the new system there has devolved into a partisan fight. Republicans strongly oppose it, claiming that it presents a serious risk of counting errors and that voters who don’t rank all the candidates can be effectively disenfranchised if their top picks are eliminated. Mary Mayhew, a leading Republican candidate for governor, called ranked-choice an “absolute disaster” and scoffed at the idea of reaching out to voters who are inclined to vote for someone else. “Can you imagine asking someone that?” Ms. Mayhew told The Atlantic. “No, I’m campaigning to be their No. 1 choice.”

An understandable reaction, perhaps, but it misses the point. When voters can express their political preferences more fully, the politicians they elect will be more likely to represent them more fully. And ranked-choice carries no built-in advantage for any party. For example, Maine’s current governor, Paul LePage, drew just over one-third of the vote in 2010 and most likely would have lost his primary that year if it had been held using ranked-choice. The same fate would probably have befallen Jon Tester, the Democratic senator from Montana who was re-elected in 2012 with the help of a third-party candidate who siphoned votes from his Republican challenger.

For now, ranked-choice is the system in Maine, but the battle over its use has put it back on the ballot, so voters on Tuesday will be using it as they are deciding whether to stop using it going forward.

Ranked-choice voting can’t single-handedly fix America’s broken elections, but it’s a worthwhile experiment, and it’s already proved to make for a better process, particularly in candidate-heavy primaries. If it’s combined with other electoral reforms, like multimember districts that can more accurately reflect the political makeup of a region, it could do even more to help voters feel that their voices are being heard, even if they’re in the minority. And that could help drive up turnout, which is notoriously bad in midterm elections.