They are in the news, not for the first time. Rhiannon attracted attention because of her opposition to the federal government's Gonski 2.0 school funding scheme. It apparently derailed the Greens' desire to clinch a compromise deal with the government. Rhiannon agreed with the Australian Education Union that the scheme was neither sector blind nor needs-based. Further, she outraged her Senate Green colleagues by seeming to campaign publicly against the scheme while her leader, Richard di Natale, was negotiating with Malcolm Turnbull and Simon Birmingham.

Bernardi's opposition to Gonski 2.0 attracted much less attention, because his vote was ultimately not needed. But he and Liberal Democrats senator David Leyonhjelm were the two crossbench senators who failed to support the legislation. In their case, it was on the grounds of opposition to increased government spending and support for smaller government rather than the distribution of the funds.

What did attract attention was the Australian Conservatives party's continued growth. Bernardi left the Liberals in February and, since then, has swallowed up the Family First Party by enticing its SA state representatives to join him. In Victoria, he achieved a second coup, announcing that the lone Democratic Labour Party representative in the Victorian state parliament, Rachel Carling-Jenkins, also crossed over, saying it was in the interests of greater national conservative unity.

Bernardi and Rhiannon are not alone in their respective positions. Bernardi had considerable support within the SA branch of the Liberals before he departed (he was, after all, No. 1 on the ticket) and his brand of conservatism clearly resonates with some Liberal conservatives Australia-wide. He has influential supporters and there may even be some Liberal defectors to him at state or federal level.

Rhiannon is a force within the NSW Greens, which has long had a distinctive industrial-left culture in a party that has greater state differentiation than the major parties. The NSW Greens consider themselves unique and have a long history of internal factional dissension. The NSW party is home to the socialist reform group, Left Renewal, which backs Rhiannon.

The clearest commonality between the two is that both project themselves as more principled than their respective parties. Consequently, they are described as hardliners, hard left and hard right. They reject compromise and the middle ground and are not team players. Bernardi ultimately left his party. Rhiannon is unlikely to do the same, because she would not survive an election outside it, but her party colleagues have censured her publicly.

Presumably, Rhiannon's ultimate crime was not just public dissension but a refusal to submit to the majority view once it was reached. If she had split the parliamentary party after di Natale pledged the Greens' support to Turnbull, it would have been highly embarrassing. It would have weakened the leader's negotiating strength because another two votes would have needed to be found among independents and minor parties. Turnbull took the obvious step of enlisting the crossbenchers en masse.

The second major similarity between Bernardi and Rhiannon is that both stick to a belief in social movement rather than party politics.

There is nothing new for a Green MP because the wider Green movement has always had a commitment to grassroots movement politics and a wariness about becoming too parliament-centred. Parliamentary representatives are still a little bit suspect within the wider movement, always to be watched carefully lest they become too independent of the Green base. Even party founder Bob Brown was called into line from time to time for getting ahead of the movement and for insufficient consultation.

On this occasion, Rhiannon says she was acting in the spirit of supporting the democratic decisions of local Greens groups. She authorised a local Greens leaflet that was distributed to Sydney residents.

Bernardi, on the other hand, is out of the ordinary because the Liberals have always been a primarily parliamentary party. He has a long history of wanting to counter the advantage that he sees the political left having because it is supported by wider movements, both the labour movement and modern groups like GetUp! The official Liberal organisation agrees with him but don't know what to do about it.

He set out to create such a wider conservative movement, primarily online, and has had some success. He is a modern politician attuned to social media, compared to Rhiannon who is more at home in a culture of local, participatory politics. The leaflet that got her into trouble is a case in point. She was campaigning on the ground through a letter drop by local Greens rather than running an internet campaign. Modern campaign gurus would consider her old-fashioned but there is much to be said for such a people-centred approach.

The ultimate test of Rhiannon and Bernardi's power and influence will be whether they are merely anachronisms or whether they have strong member and voter support on the left and the right respectively. In the meantime, inside or outside their parties, they remain a powerful irritant to the mainstream political leaders.

John Warhurst is an emeritus professor of political science at the Australian National University. john.warhurst@anu.edu.au