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Pauline Hanson says she’s not one to seek congratulations.

But the former federal member of parliament is claiming credit for this week’s abolition of the Road Safety Review Tribunal, protecting owner-truck drivers from a pay-rise order they argued could send them broke.

“I’ve never been one saying I want a pat on the back for this,” Hanson tells The Saturday Paper. “It’s about making a difference.”

Hanson says she raised the issue weeks ago. And this voice of politics past, hoping to return, has some powerful backing.

Broadcaster Alan Jones also credits Hanson – and himself – for the tribunal’s abolition, after she phoned his program on April 1 from the truckies’ annual Burrumbuttock Hay Run, delivering hay to drought-stricken Queensland farmers.

In truth, some of Jones’s colleagues were talking about it before that. But he is a powerful megaphone for the woman who has tried several times to re-enter politics at the federal and state level and who, this time in the senate, actually has a shot at winning.

“I run my own race. No one will be pulling my strings. I’m nobody’s puppet.”

The combination of the new senate voting system – provided a High Court challenge doesn’t see it struck down – and a double-dissolution election may work in Hanson’s favour.

A new senate analysis by the progressive think tank The Australia Institute supports her assessment.

For starters, compared with a normal half-senate election, the number of seats up for grabs when the whole senate is dissolved is doubled. So the percentage quota required to win one is halved.

The institute suggests that rather than locking out the micro parties and independents, a full senate election and the new voting system could combine in the 2016 election to see small players win just as many senate seats as they have now – or more. Now, there are eight independents. The institute predicts between five and nine after the election.

Hanson believes the new senate voting system may help her by giving voters more control over preferences and restricting the big parties’ capacity to do preference-swap deals to lock her out.

“I keep having a go, don’t I? I keep putting my hand up,” Hanson says. “I think the difference this time is the voters are in control of their votes this time. I don’t believe I’m going to be cheated out of a seat this time in where they direct their preferences.”

Some major party observers are cynical about Hanson’s motives, pointing to the fact the system provides that candidates earning above 4 per cent of the primary vote receive $2.62 per first-preference vote – a figure that will rise with inflation on July 1. Under federal electoral law, the candidate doesn’t have to provide spending receipts to claim it.

But Hanson has her own preferences strategy, urging conservative voters in Queensland who like her but still want to support the Liberal National Party to put her second.

“Liberal voters might not give me their No. 1 vote but they might give me their No. 2,” she says.

In fact, she says, “same with Labor voters” and with Greens.

If voters do what she suggests, it would ensure she receives their overflow preferences, which could be enough to get her elected.

1 . Preference deals

Under the previous senate voting system, people could either vote below the line – numbering every box – or above the line, numbering just one. More than 90 per cent of voters usually chose the second, easier option. It meant they handed control of their preferences to the party of their first choice.

Above-the-line votes are cast for a party or group. Until this year, the parties receiving those primary votes then directed which candidates received them as second and subsequent preferences by registering a ticket nominating preference flow. Backroom deals and horse-trading would dictate which candidates benefited and who was put last.

But not anymore. Now those preferences won’t flow beyond candidates from the same party or group unless voters expressly order it by numbering further boxes.

Something else is different this time, too.

In a normal half-senate election, a candidate has to secure 14.3 per cent of the overall vote to get elected – a quota based on a complicated formula. In a double-dissolution, 7.7 per cent is required.

If a party or group reaches that quota, their first candidate is elected. If they attract more than a whole quota – but not enough to secure another – the overflow percentage is redirected to whoever else the party or group chooses to receive it.

That has meant parties or candidates not achieving a quota with their primary vote could still get there with the preferences from those overflows. That’s how the Australian Motoring Enthusiast Party’s Ricky Muir ended up in the senate on a primary vote of only half of 1 per cent.

So preference deals have been crucial.

That will no longer happen without voters’ express direction. Below the line, voters will be told to number at least 12 boxes. While those choosing to vote above the line will now be instructed to number at least six boxes, it will still be valid to number just one.

An unknown percentage of voters will do that, or only number a couple more. Those votes will exhaust after those choices, without cascading down as overflow preferences to subsequent choices.

That means that by the time the last one or two of the 12 seats up for grabs in each state are being decided, not all votes will still be in play. (It is less relevant in the territories, where there are only two each.)

Because of those exhausting votes, the application of the usual formula means the last one or two seats in each state will be able to be won on a dramatically lower percentage.

Instead of 7.7 per cent, it could be as low as 3 per cent.

So rather than ensuring small parties and independents don’t get elected on a minuscule percentage of the vote – something put forward as the reason for the change – in a forthcoming double-dissolution election, the new system could actually ensure they do.

The Australia Institute’s executive director, Ben Oquist, identifies this as one of two big wildcards affecting the senate outcome at this election.

The second factor is that for the first time party logos will be allowed on the ballot paper.

This measure is designed to avoid the kind of confusion that allegedly saw some New South Wales voters in 2013 mistake the Liberal Democrats for the Liberals, electing David Leyonhjelm to the senate.

But if it’s supposed to turn voters away from those candidates, Oquist says it could do the opposite.

“Will that increase the chance of minor parties and micro parties attracting the attention of voters at the ballot box?”

Nobody knows.

2 . Leyonhjelm's chances

Leyonhjelm does not concede voters elected him by mistake. But he agrees the vote exhaustion rate could help small-party candidates secure those last seats on relatively small percentages.

He says it will be a case of “last person standing”. Smaller parties need only to have “a capacity to pick up a primary vote which is big enough to keep them alive in the count” but not necessarily secure a full-sized quota.

In Queensland, he thinks the former Palmer United Party turned independent senator Glenn Lazarus will face a challenge from Hanson, among others, for the final seat.

“I actually think there’s a very good chance of One Nation and Lazarus competing,” he says.

Leyonhjelm rates himself a good chance of staying on in NSW, and Family First senator Bob Day also a good chance in South Australia.

He says that with the disintegration of the Palmer United Party the big question is where the national protest vote will go.

Leyonhjelm says Clive Palmer told him previously he would run for the senate in Queensland.

But this week, Palmer insisted he would recontest his lower house seat of Fairfax. Few expect him to retain it.

“Clive’s finished,” Hanson says. “There is no support for Clive Palmer.”

Some in the major parties say the same about her, but she contrasts herself with the Palmer United Party. “I run my own race. No one will be pulling my strings. I’m nobody’s puppet. I’ll look at legislation on its merits.”

She says she would work with all parties. She supports Labor’s push for a royal commission into the banking sector. She is opposed to Australia signing free trade agreements and is still concerned about the international agenda on climate change.

“This whole climate change is not based on empirical evidence and we are being hoodwinked,” she says. “Climate change is not due to humans.”

Hanson’s posters proclaim: “No more mosques, Sharia law, halal certification, Muslim refugees.”

But she is critical of one politician who shares her strong views against Islam, Tasmanian senator Jacqui Lambie.

Hanson says she hasn’t had any contact with the senate maverick who has now registered her own party, the Jacqui Lambie Network. The Queenslander, who notes she was first to name a political party after herself, says the Tasmanian contest will be “very interesting”.

For one, Hanson has recently launched her own senate candidates’ campaign there. “She’s not going to be a shoo-in.”

The other prominent independent now running a team under his own name – and the one likely to be most successful – is South Australian Nick Xenophon. The Australia Institute analysis suggests his group could secure three seats in South Australia, leaving the Greens with just one.

3 . Greens and Xenophon

In South Australia, Greens members have decided by full membership ballot which of their two current senators will have top billing on their senate ticket – Sarah Hanson-Young, elected first in 2008, or Robert Simms, who replaced the retiring Penny Wright in September.

But their decision remains secret – even from the candidates – until the election is called. It’s the same in Victoria, where the two Greens vying for top spot are Senator Janet Rice and party leader Senator Richard Di Natale.

Xenophon is running senate candidates around Australia and could well end up holding the balance of power with the Greens and others.

He has been cultivating a political relationship with Lambie and other minor-party colleagues. He hopes they are returned.

“I would rather Jacqui in the senate than someone from the major parties,” Xenophon says. “I would rather [former Democratic Labour Party senator] John Madigan… I would rather Glenn Lazarus. I would rather deal with my crossbench colleagues than someone from the major parties.”

He is less keen on Hanson joining them.

“I think Pauline Hanson’s politics are the politics of division,” Xenophon says. “I don’t think that’s what Australians want or need.”

But Hanson argues she will be an asset. “The senate is going to be the people’s insurance against bad government,” she says. “If they vote correctly and put independents like myself [in]… we can actually be their insurance policy for good government. You will only get good government if you get good opposition.”

4 . Parties need to educate voters

Ben Oquist argues that to maximise voters’ power to exercise choice, political leaders should be urging those voting above the line to number every box, to ensure their votes are engaged all the way.

“I think there is a moral imperative on the parties to say loud and clear: vote as far as you can… The real education campaign comes from the political leaders.”

So far, no such campaign has emerged.

It’s also not clear what the Liberal and National parties will recommend to their voters about where to put Pauline Hanson.

They, Labor and the Greens will still have some influence over preferences because they attract enough of the vote to generate overflow and are well-enough resourced to both print how-to-vote cards suggesting an order of preference and provide staff at polling booths to hand them out.

Hanson is unfazed by what the parties recommend. “The major political parties have always put me last,” she says. “It’s not going to change. They are quite happy to take a lot of my policies but they don’t want to see Pauline Hanson on the floor of parliament.”

The Labor Party has already made up its mind.

“We have a standing resolution of the national executive that we don’t deal with the racist right, and therefore we won’t be talking to Pauline Hanson,” ALP national secretary George Wright says. “We won’t even talk to her.”