Yates, 37, confessed to police that on June 20 she drowned her children, ranging in age from 6 months to 7 years, but she has pleaded innocent by reason of insanity.
Jury selection is expected to take four to five weeks. Testimony is not expected to begin until mid-February.
The district attorney's office is seeking the death penalty. But in court on Tuesday, prosecutor Joe Owmby disclosed that the district attorney's office was willing to offer a life sentence "if Yates was willing to accept responsibility for her criminal acts."
Neither side commented on Owmby's offer; state District Judge Belinda Hill has imposed a gag order.
During general questioning by Hill in the first day of jury selection on Monday, everyone in the juror pool said they had read or heard about Yates. Nine indicated they would be unable to put aside their opinions of Yates and consider only the evidence.
Seven raised their hands when asked if anyone opposed the death penalty, a punishment jurors will be required to consider if Yates is found guilty. Three potential panelists fell into both groups.
"Simply because Mrs. Yates is here charged with two counts of capital murder by the indictment does not make her guilty of anything," Hill told them.
As the potential jurors left Hill's courtroom, Yates grinned as her husband, Russell, walked toward her from the back of the courtroom. He returned the smile but they did not speak or touch.
Before assembling in the courtroom, potential jurors filled out a 14-page questionnaire. Court officials refused to release a copy of the questionnaire, which typically asks about family life, experiences with the criminal justice system and sentiments about punishment.
Yates faces two capital murder charges: for drowning Noah, 7, and John, 5; and for drowning Mary, 6 months. Charges are pending for the drownings of the other two children, Paul, 3, and Luke 2.
Both prosecutors and defense attorneys have submitted long lists of expert witnesses to testify about Yates' mental status before and at the time of the drownings.
Yates' attorneys and her husband say she suffers from a severe form of postpartum depression. If found not guilty, she would be sent to a psychiatric hospital for treatment.
Legal experts say the question of whether her illness meets the legal definition of insanity will be a key issue for jurors.
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