One act of dishonesty may be forgiven, two becomes harder to overlook. On top of her admission that she withheld information from Social Welfare about her living arrangements on the domestic purposes benefit, Metiria Turei has been found to have enrolled for an election at a false address. It begins to look like a pattern of behaviour of a person with too little regard for the obligations of honest citizenship, and we can only wonder, what more might emerge?

The Green Party has reason to be worried, so much so it is remarkable that it stood by her yesterday when she did no more than renounce any claim to a ministerial position in a coalition with Labour. That was obviously for Labour's sake, relieving its new leader, Jacinda Ardern, from having to answer the question, would she have the Greens' co-leader in her cabinet?

That is not the only question Turei poses for Ardern. She presents Labour with a dilemma because attitudes to Turei's conduct differ widely between voters on the left and those in centre. On the left there was admiration for Turei's bold step to publicise the Greens' welfare policy, so much so that the Greens lifted their support by five points in opinion polls published last weekend, while Labour dropped by around the same margin. To recover those supporters, Ardern might not want to be too hard on Turei, but if she wants to reassure voters in the centre, she may have to take a tougher line.

The attitude she adopts will provide an indication of Labour's broader hopes following the change of leader. Ardern has made such a good start this week that already the party may have hopes of doing much more than regaining the votes lost to the Greens. With a more personable, "positive" leader it looks to have every chance of competing for the centre ground.

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Labour's ambition, no less than National's, will be to do well enough at the election that is does not need to deal with Winston Peters. Yesterday Ardern ruled out any post-election agreement that would let Peters be Prime Minister. Despite Turei's presence, she would no doubt prefer to deal with the Greens. But it would be much better for both parties if Turei did the decent thing and resigned, certainly from her Greens leadership and ideally from its candidate list for the next Parliament.

That is what National's Todd Barclay has done, though Turei and her co-leader James Shaw have been calling on him to go sooner. Having mounted a high horse against Barclay, Shaw is now in the embarrassing position of defending Turei's effort to stay. Both of them are at risk of much more emerging from the past she has opened for examination. Newshub's discovery that she was listed at the same address as the father of her child while she was on the benefit, plainly caught her by surprise. She had forgotten she gave that address for electoral enrolment so that she could vote for a friend. What else has she forgotten?

When she decided to reveal that she had not told Social Welfare she had flatmates helping pay her rent, she ought to have made sure she was telling the country everything that might emerge from media inquiries or the Ministry of Social Development's fraud investigation. She has exposed herself, her party and its election partner to continuing risk. She could put an end to it by resigning now.