Former City minister Lord Myners wants to replace this with a slimmed-down "plc and beyond" structure staffed by professionally-trained directors.
The former Marks & Spencer boss was appointed a director of the Co-operative Group in December but announced he is to leave following this weekend's vote.
He has said it was apparent to him from the first time he attended a board meeting that not one of its members had the ability to address the complex issues faced by a group burdened with £1.4 billion of debt.
This weekend's ballot will be decided by representatives of its independent societies and affiliated organisations - who hold 22% of the vote - and others voting on behalf of its regional membership boards making up the remaining 78%.
More top news
Ukip leader Paul Nuttall has announced that he will be standing for the seat of Boston and Skegness in the forthcoming General Election.
Beckie Finch and Adam Ryan met on the dating show but the groom had to track down his future missus after filming as he didn't pick her.
The Prime Minister was reportedly coming under pressure from Tory MPs in the south to cancel HS2.