“Our basic finding is quite startling,” said Maya Sen, a political scientist at the University of Rochester who conducted the study along with Adam Glynn, a government professor at Harvard.

The standard scholarly debate about how judges decide cases tends to revolve around two factors: law and ideology. “Here, we’ve found evidence that there is a third factor that matters: personal experiences,” Professor Sen said. “Things like having daughters can actually fundamentally change how people view the world, and this, in turn, affects how they decide cases.”

The new study considered about 2,500 votes by 224 federal appeals court judges. “Having at least one daughter,” it concluded, “corresponds to a 7 percent increase in the proportion of cases in which a judge will vote in a feminist direction.”

Additional daughters do not seem to matter. But the effect of having a daughter is even larger when you limit the comparison to judges with only one child.

“Having one daughter as opposed to one son,” the study found, “is linked to an even higher 16 percent increase in the proportion of gender-related cases decided in a feminist direction.”