He looked ridiculously, absurdly, like a copper. If he had been wearing full uniform, and started his conversation with the words “Hello, hello, hello and what have we here”, I wouldn't have been more convinced that I was talking to a policeman. And while this may seem like a trivial observation, I promise you it isn't. The fact that he looked like a copper is central to my argument.

Last Friday I was on the BBC Daily Politics programme discussing the ins and outs of the Mandelson reshuffle, when suddenly a new guest appeared and the subject changed.

The man opposite me was Lord Mackenzie of Framwellgate - straight back, commanding manner, evenin'-all moustache - and I soon discovered that my supposition that he had been with the force was correct. Having risen to the rank of chief superintendent, he was now a former president of the Police Superintendents Association. And Lord Mackenzie had a thing or two he wanted to say about the resignation of Sir Ian Blair, as Commissioner of the Metropolitan Police.

The point he wanted to make was that with the intervention of London Mayor Boris Johnson, the commissioner's job had become a political football. His Lordship did not want “party politics” to become involved in policing. He thought “the independence” of the police was critical. We engaged in some sparring on this point for a few minutes, and then he got up to leave.

As he headed backstage, one of the other contributors to the show turned to me and whispered: “I thought you were going to point out that he is a Labour peer.”

“He is a what?” I replied incredulously. I have rarely been so regretful of ignorance than I was at that moment. I had just been given a lecture on the importance of the party political independence of the police force by a man who takes the Labour Whip in Parliament.

However, I am not writing this column simply to point this out, just because it is a devastating fact that I failed to deploy at the right moment. No, to do that would be self-indulgent. And childish.

I am writing it because Lord Mackenzie used a common little trick that you often come across in politics. One that bedevilled the entire controversy last week about the sacking of Ian Blair. He confused two types of independence - a desirable type and an undesirable type - pretending they were one and the same. And it is that, not him, that I am writing this column to expose. Really.

The idea of independence is valued in politics because independence of mind is both rare and useful. James Surowiecki's book The Wisdom of Crowds has become famous for its assertion that large groups of amateurs are capable of better judgments than individual experts or small groups of experts. What has been forgotten is that Extraordinary Popular Delusions and the Madness of Crowds, the title of the Charles Mackay book that Surowiecki is playing off, is often a better description of how groups really behave.

What turns crowd wisdom into crowd madness is that independence is so difficult to ensure. For the average judgment provided by a large group to be wise, it is, as Surowiecki makes clear, necessary for the individuals to be making their judgments independently of each other. And they so rarely are. Even when they think that they are.

And that is why it matters that Lord Mackenzie looks like a copper. There are two reasons why he does so. The first is that he joined the police force because he looked like a policeman. the second that he looks like a policeman because he joined the police force.

If the first of these reasons seems implausible to you, consider this - an extraordinary piece of work by the behavioural scientist Brett Pelham, using the national directory of the American Dental Association, shows that people called Dennis are disproportionately likely to become dentists. It is also the case that people called Florence are disproportionately likely to move to Florida and people called Louise to move to Louisiana. Our anxiety to be with people who are like us makes us join up with others whom we resemble or sound like, even when we don't consciously realise that they do.

As for looking like a policeman because he joined the force, this is hardly unusual. Professors, football players, nurses, I could go on. Professionals look, sound and dress like each other to a marked degree. I was amused at last week's Tory conference to see how party members have begun to ape David Cameron and George Osborne. Who, of course, ape each other.

Evolutionary psychologists have a simple explanation for this behaviour. We co-operate with those who do not share our genes because it has been a successful evolutionary strategy to work with those who will reciprocate our favours. Together with those people we then compete, sometimes aggressively, with other groups. In order to create groups we trust and exclude those who should not be trusted, we conform to group norms, beginning to look and sound like each other.

So as Lord Mackenzie demonstrates (you can see it, not just hear it), independence from each other, real independence of mind, is hard to find. Even though it is very valuable. A police service where there was genuine independence of mind, rather than groupthink, would be superior - more receptive to the criticisms and ideas of others.

It was this desirable independence that Lord Mackenzie, and other critics of Boris Johnson's intervention, were trying to evoke. Unfortunately, it is not what they meant. What they meant was not that they wanted police to be more independent of each other, but that they wanted them to be more independent of the voter. And this is ironical.

For what is the one way to ensure that small groups of individuals, all thinking the same, serve the public good and not just each other? It is to make them accountable to a very large group of extremely diverse people, each with a small but different stake in the outcome. In other words, democracy.

Political accountability is not perfect. Even very large groups, such as millions of voters, are not truly independent and suffer from groupthink. In representative democracies, politicians can form little groups and not be as independent of each other as good decision making would require. But democratic accountability, for all its imperfections, is still superior to allowing a profession, such as the police, effectively to manage itself.

In the Blair case the idea of independence, a noble one, is being turned upon itself. The police are asking to be independent of public management, so that they can carry on being too dependent on each other.

This is an argument that must be resisted. And I am glad that Boris Johnson has resisted it.

daniel.finkelstein@thetimes.co.uk

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