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%.
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The 81-year-old revealed she wasn't asked to follow the hit TV show to Channel 4, and wouldn't have been tempted by the money.
Minister will fail to eliminate the gender pay gap in a generation if it continues to "ignore" evidence to help achieve its goal, MPs warn.