MEXICO CITY — One spent more than five years in a U.S. prison for trying to smuggle meth. Another was embroiled in a scandal involving journalists shot dead. At least four have faced investigations for offenses like sexual abuse or organized crime.

These are just a few of the candidates vying for judgeships and magistrate posts in Mexico’s first judicial elections on Sunday, which are set to transform the nation’s judiciary, including the Supreme Court.

The overhaul has opened the door to more than 7,000 candidates, shifting from judges being appointed to a system where voters elect judges.

And there are few requirements to run.

The changes were pushed last year by outgoing President Andrés Manuel López Obrador and backed by his successor, President Claudia Sheinbaum. They have argued that the measure would infuse the judicial branch with more independence, root out corruption and, by allowing citizens to select judges, democratize the judiciary.

But some critics and legal experts said the move could instead erode judicial independence and expand the sway of the governing Morena party. They say the election to fill 2,681 judicial posts risks turning the courts into a politicized body defined by popularity, not legal expertise, and more vulnerable to outside influence.

Criminal groups have already infiltrated local governments, security forces and sectors of the economy in large parts of Mexico. That candidates accused of criminal ties will appear on the ballot has fueled further fears that organized crime has found ways of “ensuring that its tentacles will reach into the judicial system,” said Amrit Singh, a professor at Stanford Law School who has analyzed Mexico’s experiment.

“It’s very easy to imagine a situation where organized crime would get to influence the elections, directly or indirectly, and the votes that a judge receives.”

Morena leaders have publicly downplayed the risks, calling the presence of some candidates simple “human errors.” Sheinbaum has also dismissed concerns, defending the system.

“Every process is perfectible, every single one. But from our perspective it is better to do it this way than what we had before, or what we still have today, where there is nepotism and corruption,” she said last month. “We’re talking about a tiny, minuscule percentage of all the candidates who went through the vetting process.”

But members of Sheinbaum’s party have tried to block some candidates.

“We missed some cases,” Gerardo Fernández Noroña, the president of the Mexican Senate and a Morena member, told reporters in April. “They should not participate. They do not comply with the constitutional requirement of probity.”

Under the old system, to be appointed a judge, a candidate needed to be internally promoted based on exams, training and performance evaluations. The rules were meant to ensure qualified candidates, but they did not prevent problems like corruption.

To get on the ballot for Sunday’s election, people needed to meet a few basic requirements — a law degree, some professional experience and a clean criminal record. They were then evaluated by selection committees, groups of experts assembled by each branch of government and tasked with identifying the most qualified candidates.

It is unclear how some people who did not appear to meet the criteria made it onto the ballot, and supporters of the election have acknowledged that tainted candidates slipped through.

In letters seen by The New York Times, the presidents of both houses of Congress — where Morena has supermajorities — asked the country’s electoral authority to exclude 18 candidates they said did not meet the constitutional requirement of having a “good reputation.”

The attorney general’s office has investigated at least four of the candidates for such crimes as sexual abuse or organized crime, according to the letters, sent in early May. Two more had worked as defense lawyers for cartel members. The rest were suspected of involvement with criminal groups or having favored them.

“Failure to cancel the registrations of such candidacies would seriously compromise the jurisdictional function,” the letters said. But under the new regulations, the National Electoral Institute, the agency that organizes elections and oversees voting, can only review and disqualify candidates after Election Day.

The institute will evaluate the profiles of the candidate who receives the most votes in each contest. Factors like having a criminal record, being a registered sex offender, being wanted for a crime or having a history of domestic violence could disqualify some candidates, potentially leading to their removal.

“Of course we are appalled by the fact that someone defended drug traffickers,” said Norma Irene de la Cruz Magaña, a member of the institute’s governing council. “Is that enough to disqualify them? I don’t know.”

Fernando Escamilla, a 32-year-old candidate for state criminal judge in the northern state of Nuevo León, once offered legal services to Miguel Ángel Treviño, a notoriously brutal leader of the Zetas cartel, and Eleazar Medina-Rojas, another high-ranking member of the same cartel.

Escamilla has acknowledged working for Medina- Rojas. But he said in an interview that in the case of Treviño, who was captured in Mexico in 2013 and is believed to be responsible for the killings of scores of people, he merely provided legal advice on extradition laws to the defense team.

Disqualifying him for this reason, Escamilla said, would be “unfair” and “discriminatory to the free exercise of the legal profession,” adding that all Mexican citizens have the right to an adequate legal defense.

“It’s like a doctor,” he said. “When patients arrive at the emergency room, the doctor doesn’t ask what they do for a living before deciding whether to treat them, they just do.”

Unlike in the United States, where lawyers must follow strict codes of conduct or face disbarment, Mexico’s bar associations have little oversight of their members. While many lawyers representing people with criminal ties operate within legal bounds, others serve as key intermediaries between cartels and business leaders or corrupt officials, and even help coordinate illegal operations.

Screening officials have defended their work, saying they requested criminal records and background checks for candidates.

“We were exhaustive in gathering all this information,” said Andrés García Repper, who participated in an evaluation committee and is a candidate in Tamaulipas state. “If two cases out of more than 12,000 seep through, well, that speaks to the effectiveness of the committee’s work.”