There’s a better way. Mr. Schwarzenegger and other reform-minded Republicans ought to create a new party that can woo independent voters, former Republicans and even disaffected Democrats. At the start of this year, barely a quarter of registered voters in California said they were Republicans, down from more than a third in 1997. At the same time, the number of voters in the state who say they have no party preference has more than doubled, to about 25 percent. This strongly suggests that most people who have left the Republican Party have not become Democrats and would be open to a center-right political party.

If a new California-based party can win votes and legislative seats, it could send a signal to politicians around the country that moderation can be a bankable political strategy, helping to break the vise grip of tribal politics that has turned so much of national politics into a blood sport and made it impossible for Congress to pass substantive bipartisan legislation.

American politics has tended to be hostile terrain for the idealists and romantics who have started third parties or mounted independent campaigns for the presidency, governorships and other elected positions. Most such efforts fail, and political experts say that a Californian third party made up primarily of former Republicans would have difficulty raising money. Many conservative donors would fear alienating congressional Republicans from California, like Representative Kevin McCarthy, the House majority leader, who is angling to be the next speaker. What’s more, there may not be enough politicians willing or able to spend years in the political wilderness building a durable party.

That said, if a third party has a chance anywhere in the United States, it’s in California. The state allows the two candidates who get the most votes in a so-called open primary, regardless of party affiliation, to advance to the general election. This should, in theory, make it easier for centrist and independent candidates who appeal to both right and left, like Mr. Schwarzenegger, who has never neatly fit into the Republican Party and is often the target of potshots from Mr. Trump. One former Republican, Steve Poizner, is already running as an independent for state insurance commissioner, a position he held from 2007 to 2011. That decision seems wise, given that the Republican candidates for governor and senator will probably not be among the top two vote-getters in the state’s primary on June 5.