(Image: Mitchell Squire/Private Media)

With a Labor victory of one kind or another looking more than plausible, consideration is due to the shape of the new Parliament and what it might mean for the legislative agenda of an Albanese government.

Most of the attention in this respect has focused on the prospect of a hung parliament, and while this is understandable up to a point, it overlooks the all-but-equal power of a Senate that Labor will assuredly not control even in the event of an extravagant landslide win.

The mechanics of the Senate electoral system are bewildering to many, but they are easier to get a handle on by boiling the contest down to left-versus-right, with Labor and the Greens in the red corner and the Coalition, One Nation and potentially the United Australia Party in the blue.

With each state electing six senators at a normal half-Senate election, the typical result involves an even division between the two, with the Greens commonly taking one of the three left seats and one populist or another sometimes doing so on the right.

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What can fundamentally change the Senate balance is if a given state tips over from three-and-three to four-and-two.

Maintaining the left-versus-right simplification, this can be understood using the two-party-preferred concept familiar from the lower house.

A fair chance of a four-and-two result arises if either the Coalition or Labor wins the two-party preferred by more than 57-43, since a half-Senate election quota is one-seventh and four-sevenths equals roughly 57%.

Such was the case in Queensland in 2019, when the Coalition won 58.4% of the two-party-preferred in the House of Representatives and the Senate result duly delivered three seats to the Coalition plus one to One Nation, with Labor reduced to one and the second left seat going to the Greens.

Since the senators elected in 2019 are not up for reelection, the legacy of that result means the left needs to do better than parity in one state or territory if Labor and the Greens are to account for half the Senate numbers, and two if they are to achieve the actual majority needed to pass legislation.

In this respect at least, the polls don’t look that promising for Labor, since trend measures don’t suggest Labor will breach the 57% threshold in any mainland state (leaving aside Roy Morgan’s implausible state breakdowns, and excepting Tasmania where little data is available).

However, the momentum behind teal-ish independent David Pocock does raise the prospect of an unprecedented result in the Australian Capital Territory in which its two seats both go to a broadly defined left at the expense of arch-conservative Liberal Senator Zed Seselja.

It’s at this point of the analysis that the left-right oversimplification can no longer be sustained, as there are two players who cannot be so easily categorised: Jacqui Lambie and Nick Xenophon.

Lambie reduced Tasmania’s Liberals to two in winning her seat in 2019, such that she already redresses the Queensland imbalance if we take the view of her expressed here recently by Guy Rundle that “the thing has become its opposite”.

Such is Lambie’s star quality that there seems a strong chance of a repeat result delivering a second seat to the Jacqui Lambie Network via its Tasmanian lead candidate, Tammy Tyrrell.

Similarly, success for Xenophon’s comeback bid in South Australia could well reduce the Liberals to two seats there, leaving two for Labor and one for the Greens.

So while a Labor-Greens majority looks unlikely, there are three pathways to a result that would allow an incoming Labor government to negotiate with centrist crossbenchers.

By the same token, each is uncertain in its own right: Lambie’s vote-pulling power may prove non-transferable, Xenophon’s star has surely dimmed since his failed foray into state politics in 2018, and history is not on Pocock’s side.

Should none of them come through, an incoming Labor government could face the unenviable prospect of Senate obstruction at the hands of a unity ticket of the Coalition and One Nation.

William Bowe is conducting paid consultancy during the federal election campaign for Climate 200, which is helping fund independent candidates who support policies to promote renewable energy and mitigate climate change.