“I’ve always been a dreamer,” says Caitlyn Jenner in the three-minute video with which she launched her run for the Governorship of California this week. But is the Olympic gold medalist and reality television star’s candidacy anything more than a pipe dream?

Jenner is running to replace Gavin Newsom, the slick-haired Democratic governor who faces a recall vote against a backdrop of the pandemic, among the strictest lockdowns in America, rising crime and record homelessness. A long-standing Republican and maybe the best-known transgender person in America, her candidacy is interesting for a number of reasons.

The likelihood that she will be the next leader of California is not one of them. Jenner’s candidacy could flatteringly be described as a long shot. Newsom’s approval rating is 53 per cent, and the recall vote requires a majority of Californians to agree that the governor should be recalled before any other candidates get a look in. California is much more solidly Democratic state than it was when Republican Arnold Schwarzenegger was first elected 18 years ago.

Worsening the odds further, other formidable Republicans have thrown their hats into the ring: the former San Diego Mayor Kevin Faulconer has a moderate, blue-state-friendly track record; John Cox’s stump speeches feature an actual, real-life bear. And judging by Jenner’s interview with Fox News’s Sean Hannity this week — in which she cited the owner of a private plane at her airport hangar leaving California because he “can’t take” seeing homeless people as evidence of the state’s decline — her political antennae still need fine-tuning.  (So far, Jenner has made the vague promise of “compassionate disruption” to reverse the state’s slide.)

However, as someone lauded by liberal America for her bravery when she announced she was transitioning in 2015, Jenner-the-candidate could prove to be a formidable force in the culture wars. Her candidacy may be unlikely to lead to the governor’s mansion in Sacramento, but it will go a long way to defining what it means to be conservative and transgender.

This week, the Olympic champion said she thought that children born as a biological boy should not be allowed to compete in girls sports. “Don’t sweat it. America has bigger problems than pronouns,” she responded when she was “misgendered” by a television presenter. Jenner exudes a live-and-let-live breeziness where trans activists have a reputation for the humourless enforcement of an ever-changing set of rules. Meanwhile, the American left is bound to say all sorts of disparaging and revealing things about what opinions it is legitimate for Jenner to hold.

If Jenner’s candidacy promises to be an interesting culture-war flashpoint, it is also a test of the political power of celebrity after Trump. Jenner has hired Brad Pascale, who ran Trump’s 2016 campaign. But Trump is not the only, or even the best, blueprint for Jenner’s candidacy. No, the closest precedent is the twenty-first century’s original celebrity-politician: the Governator. Not only did Schwarzenegger successfully run as a Republican in California, he also did so in a recall election against a Democratic incumbent.

The continuing trend of celebrity politicians is really part of a bigger story: the evaporating line between celebrity and politics. Actors and sports stars are a lot less shy about their political opinions than they once were. The Oscars has the preaching of a political convention and a political convention has the glitz and glibness of the Oscars. Increasingly, politics is fame and fame is politics. Forgive me a grumble, but the result is a shallower, less constructive, political culture.

The internet and the collapse in trust of institutions have combined to flatten the hierarchies that once ruled American public life. The result is one big stage on which Senators, Governors, late-night talk show hosts, YouTubers and reality TV stars are all clamouring for our attention. “Think of Jenner’s run as a reality show by other means,” was Politico’s depressingly accurate summation of a candidacy that will be parsed by cable news, social media and, well, those of us who write about politics.

The watchword is relevance: never let yourself slip out of the conversation, and Jenner’s gubernatorial bid means that, with her family’s voyeuristic television programme Keeping up with the Kardashians entering its final series, she wont’t leave the limelight. In the meantime, American politics gets a little coarser, we all get a little dumber and they all get a little richer.