STOCKHOLM — The Swedish Academy, which awards the Nobel Prize in Literature, was hit this past week by one of its worst crises in decades after three members walked out and a fourth threatened to quit in the wake of abuse accusations against a cultural figure with close ties to the institution.

On Friday, the academy members Klas Ostergren, Kjell Espmark and Peter Englund said they were leaving their seats. A fourth member, Sara Stridsberg, said she was considering doing so.

But the academy has 18 members who are elected for life, and there is no provision for resignations, meaning the seats of those who quit remain unfilled until their deaths. If one more member walks out, however, the academy will no longer have the 12-member quorum required to vote in new members.

Per Wästberg, chairman of the Nobel Prize Committee, said the Nobel Prize was not at risk.

“For that you only need a simple majority and you have a quorum when eight members are present.”