Cunliffe attracted the most support, on 29 per cent.
However, by far the most startling aspect of the poll was that MP Jacinda Ardern was in second place on 15 per cent.
Jones was on 11 per cent, Robertson on 10 per cent and Little on 9 per cent. (Little has now ruled himself out of the race).
This appears to show that voters are well ahead of the Labour Party in their desire to see women political leaders.
The startling poll results should be sparking debate within Labour and more broadly, but the significance of Ardern coming second in the poll appears to have been completely overlooked.
Labour, in fact, is in danger of looking old-fashioned and out of touch in the image it presents to the country.
Voters have become used to seeing male and female co-leaders working together in the model used by the Greens and by the Maori Party.
If Labour does indeed select a male as its next leader, it is vital that this is balanced by the caucus choosing a woman as deputy leader.
In addition, Labour should be cognisant of New Zealand's racial diversity.
Jones confirming that he is throwing his hat into the ring has added some much-needed racial diversity to the contest. New Zealand has not yet had a prime minister who is Maori, Pasifika or of other than Pakeha identity.
But statistics tell us that racial diversity is a growing feature of our country.
As well as gender diversity, Labour therefore needs to present a leadership team which is racially diverse.
If it sticks with the tried and true combination of two white men, increasingly large sections of the population will be unable to identify with the face of Labour.
This is exactly what is happening to the Republicans in the United States. They have been unable to adjust to their country's rapidly changing demographic and, in particular, to the growing percentage of Hispanic voters.
The Republicans have accordingly been punished at the ballot box because they are out of touch with voters.
Labour should learn a lesson from this.
In July last year, the media ran pictures of a Labour caucus retreat at which outgoing leader David Shearer, deputy leader Grant Robertson and MP Iain Lees-Galloway were pictured dressed almost identically in dark grey vests.
When I looked at the pictures, I was not concerned about the alleged fashion faux pas - I thought that the three white males presented to New Zealand as the face of Labour looked outdated and unrepresentative.
New Zealand's future is diverse. If Labour wants to be part of that future, it needs to present to voters leaders with whom they can identify.
Catriona McLennan is an Auckland lawyer and writer.
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