Can a political party have two leaders, or is this to misunderstand fundamentally the point of political leadership?

This is not the question Caroline Lucas set out to answer when she announced she would be standing as Green party leader on a joint ticket with Jonathan Bartley. They are running under the banner The Power of Working Together, hoping to advance a new kind of politics, in which parties cooperate in order to bring about changes that they could not effect alone.

Its first principle is that we will never get the change we need without electoral reform, so that should be the point on which politicians who disagree fervently on other things can unite.

As a sort-of declaration of sort-of interest, I support this idea of a progressive alliance entirely. The Labour members who are with her – Lisa Nandy, for instance – represent, for me, the best hope for a party that is otherwise riven by exactly the sort of alienating, cliquey, binary, uncreative “I can’t share a platform with X because they once shared a platform with Y” thinking that Lucas identifies as a core obstacle to change.

However, it’s a slightly disingenuous segue: in pitching to lead her party as a jobshare, she’s not reaching out the hand of friendship to a person of a different view. Bartley is, of course, work and pensions spokesman of her own party. Instead, she’s modelling a greener way of doing politics.

She is also rejecting the idea of a leader as a single charismatic force who imposes order along authoritarian lines but commands enough loyalty to leave her colleagues bolstered rather than weakened by their subjugation. Whether or not this jobshare leads to better cooperation with Labour, the SNP et al, is secondary. The primary case is that the party is living its values.

I always thought this was the subtext to Lucas stepping down for Natalie Bennett to become leader. Lucas said at the time, in 2012: “I want to give other people the opportunity to get well known, to have some profile in the party, hopefully to use that to get themselves elected as well.”

This was a nod to the fact that, when you only have one MP, it is a waste of potential airtime for that MP to also lead the party. But there was an underlying sense that she didn’t want the party to become the cult of Caroline – that the very traits other parties, especially minor ones such as Ukip, rejoice in finding in one person (charisma, likability, authenticity, humour, humanness), were distractions from the pressing work of talking about the world at a meaningful level.

Bennett’s leadership was an experiment in anti-charisma – not because she didn’t have a personality (she’s actually very funny) but because she was determined for that not to be the point. It was laudable, but it bombed. While people claim to despise the politics of personality, without it the message seems dry and technocratic – undemocratic, almost, like being addressed from a long way away.

It has implications for the workplace, especially for women, if a high-profile job is split and that is seen to work

Tangentially, it has implications for the workplace, especially for women, if a very high-profile job is split and that is seen to work. That again is slightly disingenuous, since the point of a jobshare is for both people to work part-time and have room for a life outside. I bet Lucas and Bartley would, in the honoured tradition of part-timers, work like dogs, and the party would effectively be getting two people for the price of one.

I don’t have a problem with that (on this rare occasion). Nor do I have a problem with experimentation. They weren’t comfortable with a single figurehead, and they couldn’t make it work with no figurehead; there’s nothing unreasonable about trying two. But it is important to be clear on motive: the truly radical thing the Greens are trying to do is not to work with other people (it’s a given that they’d have to do that, with no prospect of parliamentary majority). Neither is it to modernise the workplace. It is to create a party that is progressive in its DNA, which means participation not obedience, horizontal rather than vertical structures, a movement rather than a leader, all wave and not so much surfer.