I'm not going to claim this is an original thought. The idea came from a post on Paul Burgin's blog earlier today entitled "Accountablity" but I hope Paul will take it as compliment rather than as deliberate plagiarism if I say that I think the question merits further examination.
Paul's rather drastic solution to the Government's current troubles is to suggest that Gordon Brown should try to draw a conclusive line under the dodgy donations affair by sacking everyone involved, namely Harriet Harman, Peter Hain, Jack Dromey and Jon Mendelsohn. You would probably have to add Wendy Alexander to the list as well, though Paul doesn't mention her by name.
There are some obvious attractions to such a strategy, primarily that it would rid the Government and the party of a lightweight deputy leader and a treasurer who doesn't seem to know what day it is, let alone who has given the party money. But the key political question is: would it work, or would in fact serve to deepen Mr Brown's difficulties?
As I have said on Paul's blog, there are to my mind two major pitfalls with Nights of the Long Knives. Firstly, by sacking people you have only recently appointed, you call your own judgement into question. Secondly, some people know where so many bodies are buried that getting rid of them is likely to prove counter-productive.
Jack Dromey is a real case in point here. He was, of course, the man who blew the whistle on the cash for honours affair that hastened Tony Blair's departure, and if the Gospel according to the Blairites is to be believed, he was acting on the direct orders of Gordon Brown in so doing.
If this version of events is true, it makes Dromey unsackable, as the one man in British politics who could prove beyond any reasonable doubt that Brown plotted to bring down Blair.
On the more general point, while reshuffles have become a time-honoured way for Prime Ministers to "relaunch" their governments, recent history seems to suggest that the tactic very rarely works.
The best historical analogy would be Harold Macmillan's Night of the Long Knives in 1962 in which he sacked a third of his Cabinet - "the wrong third" as some commentators said at the time. It did him little good in the longer term, and caused one Tory MP to wryly observe: "Greater love hath no man than this, that he lay down his friends for his life."
Finally, it seems to me that if Gordon is looking for scapegoats for the current political mess he finds himself in, Messrs Harman and Hain are no more deserving of the sack than Ed Balls and Douglas Alexander.
It was they who really kicked off the current crisis by over-egging the speculation about an autumn election and whipping the media up into such a state of frenzy over it that it virtually guaranteed a backlash.
I do however think that Gordon could strengthen the government by making Jack Straw Deputy Prime Minister, as he should have been from the start, and by bringing back Alan Milburn as Minister without Portfolio to oversee some fresh thinking about a Labour fourth term, including a drive to improve social mobility.
The problem, in my view, with the Brown Cabinet is not that it contains too many incompetent minsters, so much as the fact that it contains too many kids.