Green Party members are being balloted on whether to abandon a co-speakers set-up in favour of a single leader.
The issue splits the current principal speakers
The party has traditionally avoided a single figurehead - and some members feel it marks them out from mainstream political parties.
But those in favour of the change say the party needs an identifiable figure to get its message across.
The first ballots went out on Tuesday to the party's 7,000 members. The poll closes at the end of November.
In recent years environmental issues have moved to the top of the political agenda, but although the Greens have seen an increase in councillors, there is still no sign of a breakthrough at Westminster and they lost seats in the Scottish Parliament.
Those who support a single leader say it is particularly important that the party makes its voice heard and points out weaknesses in green policies of the mainstream parties.
They point to a YouGov poll of 2,127 adults across the UK in October, which suggested 84% of people think the party should have a single leader rather than its current "principal speakers" system.
Former Green principal speaker Sian Berry, the party's candidate for Mayor of London, said: "Our proposal is to introduce clear, accountable Green leadership.
"People relate to other people, not to abstract ideas. And this poll is invaluable because it demonstrates the views of the public so clearly - and, in the end, they are the people we are accountable to."
But others disagree - Penny Kemp, a former national chair of the party, told the Guardian: "The last thing I want to see is the party splitting itself apart over this issue."
She added: "Green politics is all about eco-politics, not ego-politics. It would be very sad if the Green party turned into 'follow my leader'; we're more intelligent than that. "
There are also fears that by adopting a more traditional system, the party will become less radical.
The issue even splits the current principal speakers - Derek Wall has warned that the party should not be "sucked in" to having a single figurehead and has said "ego-led" politics has the potential to corrupt.
But his co-principal speaker, Caroline Lucas has said she supports "a more effective Green Party" with an "accountable leadership model".