But the party's 7,000 or so members are being asked whether they should fall into line with the other parties and elect one person to be in charge.
The debate within the party has been passionate and has exposed deep divisions over how the Green should run their affairs.
Our reporter Chris Mason's been speaking to leading Greens on either side of the argument. But he begins with the moment when it looked as if the party just might change the face of British politics.
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