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Monday's row between Ed Balls and Barry Sheerman on the new Children's Commissioner Maggie Atkinson is partly about the respective ambitions of Mr Balls and Mr Sheerman, of course, and underlying tensions over Prime Minister Gordon Brown.

But there is also a question about the power of select committees, much championed by Mr Brown in his early days as PM.

One of the most interesting developments at Westminster this autumn will be the proposals from the committee chaired by Tony Wright on reform of the House of Commons which was set up in July.

In particular, they are chewing over an idea that has become highly fashionable in recent months - that members of Parliamentary select committees, and the committee chairmen, should all be elected by secret ballot of the whole house.

Secret ballots are now in vogue, of course, following the election of the new Speaker by that process over the summer - for the very first time.

Such a reform could hugely reduce the power of the whips - not just in ending their ability to appoint the members of select committees, whose job is to examine the work of government (in effect the government picking its own scrutineers).

It would also in reduce the whips' overall power exercised through patronage. Until now, troublesome MPs could often be brought into line with the enticement, for example, of a place on the paper clips select committee.

Mr Wright's committee is going to have to get a move on. A big issue is how to set up elections by secret ballot without granting a simple monopoly to the party which has the most MPs (and is therefore the government party).

At present the system allows for the opposition party to chair some select committees, and even the odd Lib Dem (such as Alan Beith and Phil Willis).

So Mr Wright's committee has enlisted the help of two academics from Nuffield College, Oxford - Iain Mclean, politics professor at Oxford, and Scott Moser, a young American mathematician who specialises in game theory and the politics of choice.

They are trying to devise various election systems, using clever mathematical formulae, which would share out the committee chairs and the committee memberships so as broadly to reflect the composition of the House of Commons.

Contrary to what one might think, it is a lot easier to devise a fair system to elect members of the committees secretly than it is to elect chairmen by secret ballot.

Once you have decided the proportions of each party on each committee - a ratio of 10:7:2, for example - it is fairly easy to arrange for each party's MPs then to decide by secret ballot who serves on that committee for their own party.

Much harder is how to choose committee chairs by secret ballot. How does one share out the chairmanships? Who is to decide which chairmanship should go to which party, and how precisely is that decision made?

Also, there is the problem of what to do about the smaller parties - the SNP, DUP, Plaid Cymru and so on - as well as the increasing number of independent MPs.

How do these smaller entities get their fair share of chairmanships? There is a danger they will fall victim to a stitch-up up the big three - Labour, the Conservatives and Lib Dems.

Meanwhile some Commons committee clerks fear that if chairmen are chosen by secret ballot the MPs elected to such posts may not always mesh easily with the members of the committee (also elected by secret ballot), and one could see a clash of mandates.

Some clerks fear secret ballot elections might also attract unsuitable big-name, publicity-seeking MPs to go for these increasingly high-profile posts - members who do not have a command of the subject area or the respect of the other members of the committee.

Mr Wright, who is standing down at the next election, carries a huge responsibility in his final months in Parliament.

There is a big mood in the current climate for radical reforms, and I suspect most MPs would agree in principle with the idea of secret ballots for both the chairs and members of select committees.

If Mr Wright and his colleagues get the system right then it could radically shift the balance of power between Parliament and the government, between the legislature and the executive.

The trouble is it is all being dreamt up very quickly. Prof McLean and Dr Moser plan to report to Mr Wright by the end of this month, ready for him to deliver his report in November.