According to court documents, the typical payment to a voter was $10, a sign of the extreme poverty in the Rio Grande Valley, which is home to some of the poorest counties in America. Two of the three women — Rebecca Gonzalez and Guadalupe Escamilla — are accused of paying some voters as little as $3 for each of their votes. One voter was given a pack of cigarettes. Others were taken to buy drugs after they received cash for voting for a politiquera’s candidate.

Ms. Gonzalez, Ms. Escamilla and the third woman, Diana Castaneda, said the candidates and their campaign managers would give them the cash and instruct them to use it to pay voters in the 2012 primary and general elections, the F.B.I. said in court documents. The three women worked for several candidates running for seats on the board of the Donna Independent School District, though court documents do not identify any candidates or campaign managers.

No candidates have been arrested, although the investigation continues in an area that, unlike most of Texas, is overwhelmingly Democratic. Days after the three women were arrested in December, one of the four Donna school board members who won re-election in 2012 — Alfredo Lugo, the board’s president and a former administrator at a nearby school district — committed suicide at his home. Officials have declined to talk about the motive, and a spokeswoman for the F.B.I. said she could not comment on whether Mr. Lugo had been a focus of the investigation.

Lawyers for Ms. Gonzalez and Ms. Escamilla declined to comment, and several candidates who ran for seats on the school board in 2012 did not respond to requests for comment. Ms. Castaneda, 48, the widow of a former Donna police chief, said in a statement that the allegations were not as clear-cut as they appeared.

“Not all politiqueras do illegal or inappropriate payments to buy votes,” Ms. Castaneda said. “There are many who walk a straight line. People know me as a people person who would take pennies out of my pocket to help those in need.”