Mexico is a relatively young democracy that emerged from single-party rule less than three decades ago. Under Mr. López Obrador’s presidency, analysts warned that it was moving back in the direction of competitive authoritarianism, in which the ruling party uses the power of the state to tilt the playing field in its favor.

Mexican voters headed to the polls on Sunday to begin picking judges in an unprecedented election that could give President Claudia Sheinbaum broad influence over a revamped judiciary, the only branch of government her leftist party doesn’t control.