As part of this, Will Straw has written a new paper, extending the argument for primaries which he and Nick Anstead made in their Fabian pamphlet 'The Change We Need'.
The paper seeks to address criticisms including that made by Stuart White here on Next Left.
Jessica Asato writes on LabourList, addressing the most common objections to primaries. Long-standing advocate of primaries Anthony Painter has blogged on the campaign too.
I have also written a short commentary for Progress. At present, there are hopes and fears about what primaries would mean. I think we should hold some pilots and experiments to test these, so we can have a more informed debate after the next election.
It would make sense to use the opportunity of the increased number of late retirements to experiment with some late selections in this Parliament.
If Labour is considering primaries, then there is an especially strong case for a primary to select the next London Mayoral candidate. David Lammy, having argued for primaries in a Fabian lecture over a year ago, wrote in the Standard on Friday advocating primaries for the London Mayoral selections ahead of 2012.
Imagine if the parties held a primary election in every London borough. Candidates would have to campaign across the capital, building momentum, borough by borough, community by community. No longer could politicians get away with just campaigning in their heartlands. No longer would Labour voters in Hillingdon or Havering feel ignored by those at the top, since their votes would count for just as much as a Labour voter in Hackney. And yes, it would work the other way round, too, with Tory voters of Newham having their say in their selection.
The Guardian's Dave Hill saw this as a Lammy bid to run but also wrote on the merits of London primaries as perhaps the best way to engage in and resolve the party's debate about its London strategy.
As open a selection as possible in the 2012 Mayoral cycle could both maximise Labour's chances of retaining City Hall and be one of the most important ways Labour could start to engage with the emerging 'movement politics'.
In selecting a candidate for a directly elected position - where there is preferential and so cross-party voting - a broad range of London Labour opinion ought to be able to agree to the principle of an open contest. Indeed, if Ken Livingstone does confirm that he will run again, he would begin with considerable advantages in profile and name recognition. But I would imagine that those from the other wing of the party who are advocating primaries would have to say 'let the best man or woman win', rather than adopting an instrumental approach depending on whether they expected to do well.
But I think it would be a particularly good idea to build support on this now before the debate is dominated by which specific possible candidates might gain from such an approach - and to avoid the shambles and stitch-ups of Labour's London selection in 2000.
But perhaps primary momentum would carry us even further than that. Tom Harris says the 'inevitable consequence' of primaries would lead political parties to use a primary to elect their leaders too. He intended this partly as a warning as to whether the argument for primaries stacks up, while noting parties might find the attractions in the idea too.
Andrew Sparrow has written about this for the Guardian. He picks up on a comment which I made on Harris' thread, I expect the Conservatives would have little difficulty in replacing the current members' run-off of the final two candidates with an open vote among those who register to participate. I predict they will hold a leadership election on that model within the next 10 years. Labour would find that rather more difficult, because of its electoral college and federal structure.
There are certainly barriers to change - and questions which the primaries campaign needs to answer. But they are asking some important questions of their own too.