The Labor government is offering a referendum to change the constitution to enshrine a Voice in the constitution, but nothing yet on truth or treaty.

Fifteen of the 16 Greens MPs and senators, including its other Indigenous senator, Dorinda Cox, a Yamatji-Noongar woman from WA, chose progress by supporting the Voice. Thorpe chose none.

That’s not how she puts it, of course. Thorpe said: “This country has a strong grassroots black sovereign movement full of staunch and committed warriors and I want to represent that movement fully in this parliament. It has become clear to me I can’t do that from within the Greens.”

Thorpe, a DjabWurrung-Gunnai-Gunditjmara woman representing Victoria, says she rejects the proposed Indigenous Voice to parliament because it’s not enough: “We are sovereign and this is our land. And we deserve better than an advisory body.”

She demands a truth-telling of Australia’s Indigenous oppression and a treaty as more important than a Voice. There are two obvious problems with this position. First is that it is not on offer. There is only one proposition on offer – a Voice or nothing.

Second is that if something as modest as the Voice is rejected in this year’s referendum, no government will attempt anything more ambitious – such as truth and treaty – for a very, very long time.

So by rejecting progress towards a Voice, Thorpe is rejecting all progress. No Voice, no truth, no treaty. Emotionally satisfying, perhaps, but quite useless in making any kind of progress.

The Greens have faced this dilemma many times before. Most famously in 2009 when the Rudd government sought to act on its election commitment to create a carbon emissions trading scheme.

The Greens insisted that it didn’t go far enough and sided with the Coalition to block Rudd’s legislation. By frustrating Labor’s 2009 emissions plan, the Greens doomed progress, doomed Labor and handed control to the Coalition for a decade.

This is a case study in the impotence of purity. Lidia Thorpe evidently failed to absorb this lesson. The rest of the Greens federal parliamentary caucus learnt from their decade in painful purgatory.

When the Albanese government last year presented its legislation to cut emissions by 43 per cent, the Greens decided to shelve their unattainable 75 per cent and support Labor. In return, they persuaded the government to amend its bill to keep open the possibility of faster action.

This moved the Greens from being a protest party to become a party of progress. “The Greens were conscious that a lot of people realised 2009 was a disastrous miscalculation, and that encouraged them to engage,” as Jim Walter, emeritus professor of political science at Monash University observed at the time. “If they’d taken a hard line they would’ve been factored out.”

With Thorpe out of the party this week, the Greens swiftly decided to support the Voice and to press the Albanese government to go further. This was one of the Greens’ two main election campaign themes. One was “Kick the Liberals out”. The other was “Push Labor to go further and faster”.

This is exactly where the Greens are located now. With almost zero in common with the Morrison government, the Greens were poorly placed to achieve any of their aims.

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But now, the Liberals are out. Labor is in. Labor and the Greens share a considerable number of aspirations for change, especially on the environment and social policy, but differ over pace.

The Greens are using their leverage as the biggest bloc in the balance of power in the Senate to push Labor to go further and faster. Greens leader Adam Bandt believes that the party is ideally placed to make progress on some of its priorities by negotiating with the Albanese government. Like a fast tugboat seeking to position an ocean liner.

The Greens enjoyed their greatest electoral success yet at last year’s election. They increased their numbers in the House of Representatives from one – Bandt alone – to four MPs, three more than they’ve ever managed. In the Senate they increased their numbers from nine to a record 12.

The defection of Thorpe reduces the party to 11 senators. But they remain critical to Labor’s legislative agenda. Until this week, wherever the government and Coalition disagreed, Albanese needed to win over the Greens plus one extra senator to turn bills into laws in the Senate. Now he needs the Greens plus two.

Bandt calls it the theory of change – to intelligently use the Greens’ position in a shared balance of power to influence the Labor government.

So how does the theory apply in the case of the Voice? It turns out that Albanese’s platform position on truth, treaty and voice is identical to the Greens’. In his victory speech last May, the prime minister-elect stood at the podium at Canterbury-Hurlstone Park RSL Club in Sydney and said: “On behalf of the Australian Labor Party, I commit to the Uluru Statement from the Heart in full.”

The Uluru Statement is the manifesto from which all three elements are drawn – truth, treaty and voice. After six months of nationwide consultations, the statement was written and endorsed by 250 Indigenous delegates at the 2017 First Nations National Constitutional Convention at Uluru.

It says, in part: “We call for the establishment of a First Nations Voice enshrined in the Constitution. Makarrata is the culmination of our agenda: the coming together after a struggle. It captures our aspirations for a fair and truthful relationship with the people of Australia and a better future for our children based on justice and self-determination.

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“We seek a Makarrata Commission to supervise a process of agreement-making between governments and First Nations and truth-telling about our history.”

So by committing to the statement “in full”, Albanese committed to truth, treaty (which the Uluru statement calls agreement-making) and voice. The difference is that Albanese is offering one element only at first, cautious incrementalism. The Greens want something faster.

In agreeing to compromise, the Greens say that they extracted from the Albanese government a commitment to include funding to advance the remaining two Uluru elements – truth and treaty – into the federal budget.

With Lidia Thorpe gone, the Greens will now be able to support fulsomely the referendum for a Voice to be added to the constitution. The director of the From the Heart Campaign, Quandamooka man Dean Parkin, tells me: “In many ways, the Greens party position is clearer and in line with a lot of our supporters and Greens supporters and our focus is squarely aimed at talking to people across the board, regardless of political party.”

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The author of Inside the Greens, contributing editor to The Monthly Paddy Manning, says the Greens dodged a bullet. “Lidia Thorpe wasn’t representing Greens voters – 70 per cent of them support the Voice. If the Greens had wrecked the Voice this year, they would’ve been toast.”

A Guardian Essential poll this week has support for the Voice among Greens voters higher again – at 89 per cent.

The concluding line to the Uluru Statement says: “We leave base camp and start our trek across this vast country. We invite you to walk with us in a movement of the Australian people for a better future.”

Thorpe, a delegate to that convention, walked out on that, too.

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