Washington — For the second time in two weeks, a conservative bid to shift the law to the right fizzled at the Supreme Court, when the justices on Monday upheld the current, widely used method of counting every person — not just voters — when drawing election districts.

The unanimous ruling rejected a constitutional claim that states and municipalities may count only eligible voters when dividing up districts.

Had the court accepted such an interpretation, it would have shifted power away from cities with fast-growing communities of immigrants, including Los Angeles, Houston and Phoenix, and given more clout to suburban and rural areas. Doing so would have generally strengthened Republicans and undercut Democrats.

“History, our decisions and settled practice in all 50 states and countless jurisdictions point in the same direction,” said Justice Ruth Bader Ginsburg, explaining the high court’s decision to uphold the constitutionality of the existing practice. Political power, she said, may be divided up “on the basis of the total population.”

Liberals and civil rights advocates, who had feared a string of losses this year at the hands of the court’s conservatives, instead celebrated another victory.

Thomas Saenz, president of the Mexican American Legal Defense and Educational Fund, called the decision a “tremendous victory for democratic representation that recognizes all citizens count.” Miles Rapoport, president of advocacy group Common Cause, said it “affirms one of our most fundamental values as Americans: that every person counts.”

Ever since the February death of Justice Antonin Scalia, conservatives have been left without a crucial fifth vote, raising doubts about their ability to control the court’s rulings.

Last week, the justices said they were split 4-4 and could not decide a major challenge to unions. Conservatives had urged the court to overturn a nearly 40-year-old precedent that allows public-sector unions to collect “fair share fees” from all employees to help pay for collective bargaining. Due to the deadlock, the union’s ability to charge the fees was left in place. It’s not clear what role Scalia’s death played in the dispute over election districts, but it may explain why the decision was narrowly crafted.