How important is intelligence and education to politicians?

I ask because of Martin Amis's jibe that Corbyn is "under-educated" and "slow-minded" and Tristram Hunt's claim that it is the responsibility of the brightest 1% to "take leadership going forward." Both men seem to presume - without adducing evidence - that intellectual ability is desirable in politicians.

I'm not at all sure of this, for four reasons.

- Ability and knowledge can lead to overconfidence. For example, a study of German mutual fund investors found (pdf) that "sophisticated investors do not earn higher risk-adjusted returns." This is because they over-estimate their ability to spot good fund managers and so waste money on fees, thus offsetting other advantages that can accrue to higher intelligence. I suspect this is relevant to politics because politics, like investing, is about making judgments about an inherently complex and uncertain world on the basis of partial information. One can argue that overconfidence is a common and fatal flaw in politicians: think of Thatcher and the poll tax or Blair and Iraq.

- A high IQ can cause one to be out-of-touch with voters. Or, just as badly, it allows the media to present one as being out-of-touch. To a biased media, intellectual ability will be reframed as geekiness.

- Success in politics - and in fact in other occupations - requires more than intelligence. It requires qualities such as doggedness and an ability to get on with people - talents which aren't necessarily positively correlated with formal smarts.

- Basic ideas can work better than complex ones. As Gerd Gigerenzer has shown, simple rules of thumb (pdf) can work (pdf) at least as well as fancy theorizing. The Bank of England has suggested that this is true for financial regulation. It might well also be true in foreign policy: Corbyn's simple heuristic, "don't start wars in the middle east" isn't obviously catastrophic. And I suspect it's also true in welfare policy: a simple citizens basic income might well be superior to complex alternatives.

We don't need to look far for historical evidence here.Winston Churchill was no intellectual, but he is widely regarded as our best prime minister in large part because his simple heuristic - defeat the Nazis - was better than the more sophisticated ideas of his cleverer peers. More mundanely, Thatcher was the intellectual inferior of several "wets", but proved the more successful politician*.

All that said, there is a crucial distinction here, between ability and one's beliefs about one's ability. I would rather have second-rate politicians who know they are duffers than ones who believe they are brilliant.

Now, I don't say this with much certainty. Maybe the humble genius - if one could be found - would be an even better politician than the humble duffer. What I'm doing is posing the question to Amis and Hunt: why should one assume that intellect is a virtue in politics? Because it's not obvious.

* One could list many succesful politicians - Bevin, Major, Callaghan etc - who lacked degrees. However, in many cases this was because of a lack of opportunity, not ability, so they are not relevant to my argument.

Another thing: I am, of course, ignoring the possibility that Corbyn would have better ideas if only he were cleverer: the idea that people would all agree with us if only they were as smart seems to me to owe more to narcissism than to evidence.