The new Labor government has pledged to do politics differently, and the new Parliament contains many differences from the old: more independents and more Greens; more women and Indigenous parliamentarians and more members from non-English-speaking backgrounds. It is less pale, male, and stale and more socially representative.

The parliamentary situation of the Albanese government can be interpreted, however, as little different from the two previous Coalition governments. Its 77 seats give it a narrow majority in the House of Representatives, and it is 13 votes short of a majority in the Senate. Unlike the previous Turnbull and Morrison Coalition governments it is not restricted by nervousness about being undermined by a junior Coalition partner in the House of Representatives; but it still should proceed sensitively in its dealings with the crossbench, out of respect and in case they are needed. Like the Coalition it must negotiate with small parties and independents to pass its legislation in the Senate.

Immediately this situation raises the old notion of the government's mandate to implement its promises versus the contrasting mandate of those who hold the decisive votes in the Senate. A mandate is the authority given by the electorate to the winning party in an election to implement its promises. Equally relevant is the responsibility of the winning party to implement its policies. While the whole idea of a government mandate can be challenged, given the complexity of election results, it still has some force.

The situation also returns us once again to the recurring theme in Australian politics of the House of Representatives versus the Senate, or, in the eyes of some prime ministers, to the "People's House" versus "Unrepresentative swill". That irresolvable conflict, however described, is built into our constitution and will not change.

The other old way of doing things is the major party way, which gives majoritarian-style executive government to the winning major party regardless of the views of others. This way of doing things is embedded in the DNA of all major party politicians.

Layered over this old-style parliamentary situation are the new political and cultural realities, which are a challenge to the new Labor government (and an indirect and longer-term challenge to the Coalition opposition).

The political reality for Labor is that major parties are on the nose. Labor won 10 more seats at the federal election with a slightly smaller percentage of the primary vote. A win is a win and the decline of the Coalition meant Labor won comfortably. But it will want to consolidate its position by holding its existing seats at the next election and winning some more. Labor must play to its strengths and recognise its weaknesses.

Traditionally major parties improve their electoral position by grinding their opposition, including minor parties, into the ground, and by claiming all credit for good policies for themselves. For Labor, this means sidelining the Greens in the cities and winning more seats from the Liberals in the suburbs.

This traditional approach may not work this time around as the electorate expects the major parties to own up to their weaknesses and to do much better than previously on major issues like gender, integrity, and climate action. These are areas where the Greens and the independents have been playing the leading role. It would be a mistake for the new government to claim undue credit for any achievements when they are just catching up.

On climate action the government's "small target" of a 43 per cent cut in emissions by 2030 may come to be seen as a problem rather than an achievement during parliamentary negotiations. On integrity the electorate demands transparency and accountability, principles which all major party governments find extremely difficult to deliver.

The electorate also wants a humbler government and seem to have been impressed by Anthony Albanese's quieter style so far. Such humility must be the model for his government and the whole Parliament over the next three years.

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Beyond the raw numbers the demographic and representative transformation of Parliament calls for a new political culture. Labor's call for a new type of politics gives them an opportunity to show the way, but its history suggests that many of its factional players and hard heads will resile from this challenge and fall back on old ways.

The old-school Opposition Leader, Peter Dutton, gives no indication that he is attracted to doing things differently. Greens leader, Adam Bandt, has promised to seek the good rather than the perfect. The new teal independents have admirable models like Helen Haines and Zali Steggall to follow as they seek to find their parliamentary mojo.

What a new parliamentary culture and governmental style might look like is still unclear. Some look back to the Gillard minority government years, but the antagonistic Gillard-Abbott parliamentary arena doesn't augur well. Former Greens leader, Dr Richard di Natale, offers the New Zealand government of Jacinda Ardern as a useful model. He suggests that the Albanese majority government should act like a minority government. This would mean being inclusive by informally drawing minor parties and independents into its inner circle when issues are being discussed and policies are being formulated. Despite its merits that may prove to be a step too far, a mirage rather than a reality.