They shouldn’t be having this election now. They are doing everything in the wrong order. The nomination system stinks. The election system is neither democratic fish nor electoral college fowl. The candidates are all a bit lacking in different ways. The race for the deputy’s job is a total waste of time. And Labour is a party in denial about going through a near-death experience. Yet apart from all that, the Labour leadership election is actually looking like a good contest as nominations close today.

The good news is that there is a decent range of candidates to choose from. Two men and two women; age and youth; a spectrum of views from old left to Blairite; a mix of ministerial experience and views from the backbenches; candidates from London, the Midlands and the north. Believe me, it could be a lot, lot worse.

The other good news is that for the next three months there is a chance for the candidates to extend themselves and prove that they have the ability to operate at the highest level. The time for scrabbling for nominations around Westminster is finished. The hustings schedule starts almost immediately. But it is also a chance to think a bit, to talk to people who want Labour to succeed, to listen to advice, to think about what is happening in the world, to hone the different messages and to try on the mantle of party leadership and see if it suits them.

Female leaders can change the nature of politics in the way that men struggle to do

None of which is to say that all the worries about what is happening to Labour will suddenly evaporate. On 7 May, a Labour party that had deluded itself that it might win power under Ed Miliband was trounced in Scotland, beaten by the Tories across most of England and found its vote eroded by Ukip in many parts of the north. With few exceptions, Labour has barely started analysing what went wrong and what it needs to do to stop history repeating itself in 2020.

Miliband should have stayed on until the autumn, all the same. If he had, Labour might have had a better shot at understanding the kind of leadership candidate it needs, while giving the candidates a better chance to prove themselves. Now they are going to choose the leader and hope he or she is the right choice. If Miliband had not been so vain as to resign quickly, there might have been a chance to change the nomination system to allow any MP to stand who had a proposer and a seconder. But that’s all water under the bridge now. The party has to do the best with the system it has chosen and the candidates who have been nominated.

Of the four candidates who have made it to the starting line, Andy Burnham is the bookies’ favourite. Jeremy Corbyn’s nomination has helped Burnham because it means he can’t be so easily cast as the leftie in the race. If that had happened, it would have been good news for Yvette Cooper, who might have come through as the candidate of the centre. Burnham is still the one to beat, because the unions and the Ed Miliband supporters will gather behind him.

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Cooper and Liz Kendall will benefit from the very real feeling that it is time that Labour elected a woman leader. Personally, I think this is absolutely the case. It is time for a woman leader, and both Cooper and Kendall have things in their favour as well as much that divides them. Female leaders can change the nature of politics in the way that men struggle to do. In particular, a female Labour leader will have a lot of advantages in the 2020 election if the Conservatives are led by Boris Johnson.

Yet the two most striking nominations are really those of Corbyn and Kendall. A month ago, Kendall was barely known outside Westminster, but she was first out of the traps, has made a lot of her own luck, and has proved that there is a sizable level of support for a candidate who isn’t afraid to praise the last Labour government or to criticise the Miliband era. The question for Kendall is whether she can now push on and set the terms of the debate with genuine authority. She hasn’t done that yet. Corbyn has won his place on the ballot only because enough MPs lent him their votes. That’s an indictment of the nomination process. It will please the unbending left to have a candidate who will stand for the old-time religion. My own view is that it at least gives us a way of seeing whether there is really a strong constituency of support for electing an unelectable Labour leader. If there is, then the Labour party may indeed be beyond saving.

Nostalgics will look at the four candidates and say they don’t match up to those who stood in contests of the past. Look at 1976, when Jim Callaghan, Michael Foot, Denis Healey, Roy Jenkins, Tony Crosland and Tony Benn were all in with a shout, they will say. I don’t remember it led to a Labour election win though. And however imperfect you may find the array of candidates today, at least there is now going to be a proper argument between those who want a Labour party based on purity, those who want a Labour party based on electability – and those who can’t make up their minds about the mix between the two. It is not ideal. Nothing ever is. But it is important. And it starts today.