Caitlyn Jenner begins her campaign for California governor with a prized commodity for a candidate — celebrity. But while her name is widely recognized, what she would do in the job remains a mystery.

Nearly two decades ago, Hollywood fame helped elevate another Republican, Arnold Schwarzenegger, to the governor’s chair. But he had already made a name in state politics, working to enact hundreds of millions of dollars in funding for school programs. He once headed a fitness council for then-President George H.W. Bush, and was married to Maria Shriver from the Kennedy political dynasty.

Jenner lacks the roots Schwarzenegger had in politics, and his international celebrity far eclipsed her own. But her 3.5 million Twitter followers gives her a foothold to reach out directly to voters through social media, similar to the way Schwarzenegger could attract TV cameras from around the globe.

“It would be a mistake to view her of one of these ‘circus candidates,’ ” said Thad Kousser, a political science professor at the University of California, San Diego.

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