Even for companies that are fully based in California, the number of new female board members that the law would mandate is small. Joseph A. Grundfest, a professor at Stanford who has for years been an advocate for increasing women and minorities on boards, said he believed the law would apply to only about 72 companies that are chartered and have headquarters in the state.

“It would, at most, increase the number of women directors at the Fortune 500 by a grand total of one,” Professor Grundfest said, reiterating a point he made in a paper he wrote assessing its impact. He said the only major company affected would be Apple, which has two women on its eight-member board and would be required to add another by the end of 2021.

Smaller companies, Professor Grundfest said, could have to add as many as 208 women over the next three years, which, while not insignificant, is still only a tiny percentage of all public companies. And he believes that’s a generous estimate.

In a theoretical sense, Professor Grundfest said, he was in favor of the law. “But this is the wrong way,” he said. “I fear the cure is worse than the disease.”

The law — or, more accurately, the raft of lawsuits it will most likely inspire — could have a chilling effect on genuine efforts by boards to seek more balance. Challenges to the law could make ever-cautious corporate legal departments reluctant to have company leaders publicly state diversity goals, for fear that those statements would be interpreted as quotas. .

And while research has shown that companies with more diverse boards perform better, legal challenges to the law could take aim at those studies. The state itself, referring to three studies it used to make its case for the legislation, raised that as a red flag.

“While these studies establish a relationship between the proportion of women on corporate boards and these outcomes, it is important to note that such studies are observational in nature and do not necessarily provide evidence for a causal relationship,” a report commissioned by the state said.