If some ministers are gatekeepers, though, you would see a greater boost to your efforts at influence than the null case. Similarly, if some of them are flak catchers who mainly exist to turn away lobbying efforts, and you happened on one of those, you'd get a lesser boost. This metric should be greater than unity if the minister is a gatekeeper, 1 if they are perfectly mediocre, and less than unity if they are a flak catcher.
Interestingly, the Scotland and Wales Offices score highly. The highest value recorded is for David Jones MP, Parliamentary Under-Secretary of State for Wales, with 2.75. His closest rival is David Mundell MP, from the Scotland Office, on 1.94. The highest scoring Cabinet minister is the Scottish Secretary, Michael Moore. Some of this is down to the magic of low expectations. Nobody thinks these departments are great offices of state, not even the Welsh or the Scots - real power there has long since shifted to the devolved administrations. So if you meet any other minister, you're likely to do better. But the gatekeeper metric should handle this, as it measures influence relative to the structural difference between the minister and the average weighting. Arguably, this is a valid measurement. These ministries' role really is as a gatekeeper, something like a diplomatic representation in both directions.
So, who's the all-UK champ? It turns out to be Mark Harper MP, Minister for Political and Constitutional Reform, with an impressive 1.65, contrasting with his network degree of 0.08. Hilariously, one of his lobbies turns out to be the UK Public Affairs Council, the lobbyists' trade union, which wanted to see him in July, 2010 on the pressing matter of "lobbying".
He's followed home by Education PUSS Tim Loughton MP on 1.228, Defence PUSS Lord Astor on 1.2, Education's Lord Hill on 1.1, Justice PUSS Crispin Blunt MP with 1.09, and the sinister intellectual force that is Oliver Letwin MP, Minister of State for Government Policy, on 1.05. Francis Maude, whose horrific rise to national influence has been tracked with interest, turns out to be quite the flak catcher, on 0.43 - or is it that he claims to be a figure of authority in his own right? Does the buck stop there? After all, and as expected, once you meet the prime minister you can't really go anywhere but down.
Of course, what everyone will surely want to know is who gets the wooden spoon. Step forward Andrew Stunell MP, PUSS in the Department for Communities and Local Government, with a mighty 0.21 to go with his network degree of 0.3. Stunell held a large number of meetings around the country, notably in London, Bristol, and Bradford, as "Big Society Roundtables" with a wide range of community organisations. It would appear that nobody was more shortchanged than these. Meeting Mr. Stunell reduced one's average lobbying impact by a smacking 80%. Such was the coalition's contempt for, among other organisations, Operation Black Vote, the Stephen Lawrence Trust, and basically everyone in Bradford who showed up. The list is here.
It will surprise nobody that meeting a coalition minister would increase the UK Public Affairs Council's members' influence by 65%, but cut that of council tenants, Muslims, blacks, single mothers, young people (to list just a few) by 80%. But it's worth making it hideously explicit. And here's a lesson from all this obscure science that is easy enough to operationalise: if you see Andrew Stunell coming towards you through the Strangers' Bar with a smile on his face, don't make eye contact, don't shake hands, don't offer him your business card. Run. Spill a pint. Create a diversion. Trigger the fire alarm. Do not, in any circumstances, lobby him.
Here's the really sad bit. Stunell's dance card, from TWFY.
Voted very strongly against introducing foundation hospitals.
Voted strongly against Labour's anti-terrorism laws.
Voted very strongly against the Iraq war.
Voted very strongly for an investigation into the Iraq war.
Voted moderately against allowing ministers to intervene in inquests.
Voted a mixture of for and against greater autonomy for schools.
Voted moderately against replacing Trident.
Voted very strongly for the hunting ban.
Voted moderately for more EU integration.
Voted very strongly against introducing ID cards.
Voted very strongly for laws to stop climate change.
Voted very strongly against a stricter asylum system.
Voted moderately for removing hereditary peers from the House of Lords.
Voted strongly for a wholly elected House of Lords.
Voted very strongly for equal gay rights.
Voted moderately for a transparent Parliament.
I remember the Lib Dems. Do you? I wonder if Andrew Stunell remembers Andrew Stunell.