This is the ruling of a jury of 12 Mensa members who have created a new PQ rating - or Political Quotient, a cross between an IQ level and assessment of political acumen - to rank each member of the current cabinet.
Billed by the elite club's panel as "the brains behind New Labour", it is Peter Mandelson who finishes well ahead of his parliamentary rivals. He scores an impressive 90 points out of a possible 100 PQ.
The Trade Secretary may "not be universally liked" by his colleagues in the Labour Party, but he is considered an astute operator, without being seen as a "pointy head" (the term said to be used by Gordon Brown's spin doctor Charlie Whelan to disparage intellectuals).
Mr Mandelson is closely followed by Stephen Byers, the Chief Secretary to the Treasury, on 85 points, and Jack Straw, the Home Secretary, on 75.
Others are not so highly valued. Clare Short, Secretary of State for International Development, was downgraded for having "a mouth that is bigger than her brain". She earned only 30 PQ points and came joint bottom of the league with Nick Brown, the new Minister of Agriculture. Jack Cunningham, Chancellor of the Duchy of Lancaster, and Robin Cook, the Foreign Secretary, only just managed to beat them with scores of 35.
The PQ league table, published today in the new edition of Mensa Magazine, was drawn up during secret deliberations by an anonymous jury of specially selected Mensans, each of whom has an IQ of over 148.
The 12 panellists included several captains of industry and leading civil servants, Mensa says, and they set out to assess each cabinet member purely on political performance, rather than on their basic level of intelligence.
"Our jury took the view that some of the cabinet were too clever by half," explained Simon Clark, Mensa Magazine's editor.
"It was not as scientific as an IQ allocation, but we asked each member to rate the politician on ability and then on intellectual ability, before coming up with the final PQ figure."
Mensa acknowledges that, while an individual's IQ rating will remain static throughout their life, there is some scope for improving a PQ score. "Robin Cook did not do that well this time, but he may have learnt a lot over the last year. It is possible that next year he will score more than 35."
The chairman of Mensa, Noel Burger, said he believed his panel had been correct to assume that a powerful intellect was not the same thing as a good political brain.
"The more rounded a politician is, the more likely they are to be successful," he said. "It also is not really all that important to be liked, and here we could look at the examples of both Peter Mandelson and Margaret Thatcher."
The new edition of the magazine also carries an article by Peter Mandelson's former aide, Derek Draper, who argues that sheer intellect or "pointy- headedness", will rarely be enough to secure political advancement.
"In Britain the ambitious politico settles for a newspaper picture of himself drinking local ale in the nearest salon bar," he writes.
In contrast, politicians with less savoir-faire, such as Robin Cook, the Lord Chancellor Derry Irvine, and even William Hague, are regarded with suspicion.
He suggests that the ability to dumb down, or at least not to appear too clever, is the key to smart politicking: "Welcome Jack `The Enforcer' Cunningham, a man who learnt his trade among the shop stewards of Newcastle GMB, Peter Mandelson, a strategist with a keen intelligence, but not an intellectual, and John Prescott."
The fact that Mr Draper was recently caught out boasting about his influence over New Labour does not seem to inhibit him from offering advice.
"Ultimately it is instinct, common sense and, above all, luck which services the successful politician more usefully than any degree of grey matter," he concludes.
How Mensa Rates the Politicians
Political ability: 8
Intellectual ability: 7
Mensa says: Likeable man of genuine conviction; his common sense and decency come across.
Political ability: 2
Intellectual ability: 5
Mensa says: Responsible for banning beef on the bone. Now known as "The Enforcer".
Political ability: 2
Intellectual ability: 4
Mensa says: Mouth is bigger than her brain; lacks political finesse.
Political ability: 10
Intellectual ability: 8
Mensa says: The brains behind New Labour but not universally liked!Reuse content