Who triumphs within the triumvirate?

Power Play: The coalition leadership's first public appearance gave a taste of the dynamics around the incoming administration and the personalities that will drive it.

National's Christopher Luxon, soon to be anointed Prime Minister; energetic and no doubt relieved, leading proceedings.

On each side stood Winston Peters and David Seymour, Luxon chose not to choose between them in their first contest - for deputy prime minister - but settled on a job share, of sorts.

Neither of these characters is willing to take a back seat. After Luxon made some introductory remarks, Peters took the floor. Within a few sentences he was back to bagging the media, and was shut down by Luxon when he started to wrangle with journos in the front row.

Seymour then embarked on a lengthy list of policy wins. As he went on, Peters propped up his head with one hand looking bored; as Seymour went on, and on, Luxon nodded enthusiastically, willing him to stop.

Theatrics aside, the three have developed comprehensive agreements covering a vast array of policy, and ways and means of running the coalition, including when the inevitable disagreements arise. They are prescriptive documents, an obvious attempt to nail down as much agreement as possible in black and white ahead of whatever will come out of the blue to challenge the unity of the coalition.

Luxon summed it up as a "true three-party coalition government with a strong parliamentary majority and a comprehensive policy programme for the next three years".

The negotiations were long and tough and in some places intractable: relationships forged through the first testing times, critical to the success of this historic arrangement.

"We went to the wire for our people in the same way that David Seymour did for his and Mr Luxon did for his as well, and that's the nature of our coalition talks," said Peters.

New Zealand First secures some key policy priorities - namely the $1.2 billion Regional Infrastructure Fund, keeping the age of superannuation at 65 - as well as other policies, like an inquiry into the handling of the Covid pandemic, around gender identity, the World Health Organisation and the United Nations, directly aimed at a particular section of the party's constituency.

There are lots of plans to "investigate" and "explore" other core party policies and enough to keep its voters happy.

There's agreement for no co-governance of public services, explicit instructions to the public service about the use of te reo, and a wholesale review of references to Treaty principles in existing legislation.

New Zealand First also brings Cabinet experience to the table in the form of Peters and Shane Jones; none of the MPs in the leadership teams of National or ACT have served as ministers, you have to go down to number six on National's ministerial list to get to anyone who's been in Cabinet before.

ACT didn't get the Treaty principles referendum over the line, but has still plotted a pathway through legislation. National and New Zealand First have committed to supporting it to select committee, but from there support will have to be negotiated. Throughout the campaign Luxon has described a referendum as "divisive" but having a legislative process provides a pressure valve for the push from both of National's partners, and opportunities along the way for National - or New Zealand First - to pull the plug if it becomes too fraught.

In terms of concessions, David Seymour told RNZ the ACT Party would have "had a lot less government spending, lower, flatter taxes, taking a Treaty referendum all the way through, we would have done a lot more in changing education...". However, the range of policies it's secured balances that out.

While each deal is about 14 pages long, National emphasises the fact it has secured the support for the vast majority of its election manifesto. One major concession with significant consequences is the abandonment of the foreign buyers' tax. It was clearly a point of direct conflict for New Zealand First, which would have made it next to impossible for it to credibly support.

There was already fierce debate over National's centrepiece tax policy, whether it was affordable and whether the proposed ways to fund it stacked up. The government now has to take nearly $3 billion over four years out of the mix, the amount it intended to raise through partially rolling back the ban on foreign buyers, and taxing the purchase of luxury homes.

Luxon was vague when asked how the government would make up the shortfall; he said they had discovered "through the process that we have a buffer in our tax plan...we also have additional savings and additional revenue raising mechanisms as well".

The books are already extremely tight and the incoming government has already signalled a savings drive for the public sector, which looks like it's going to have to dig even deeper.

The next challenges for the coalition are to put together a mini-Budget before Christmas that credibly balances the books as it will have to encompass the promises made across the whole coalition deal. Ministers will also have to make sure the legislation to put the plan into place is ready to go by the time the House resumes on 5 December.

The big move will happen this weekend when Labour moves out of the Beehive and the coalition moves in.

Waiting in the wings is ousted prime minister and soon-to-be leader of the opposition Labour's Chris Hipkins who's had six weeks to hone the one-liners...

"It's good that Christopher Luxon is moving into a round office - given the circles that David Seymour and Winston Peters seem to be running around him."

Plenty to do, plenty of personalities to manage, and not a lot of time before Christmas.