Jane Martinson writes that John Humphrys "has been wearing his prejudices a bit too readily on his sleeve." Now, Mr Humphrys has his faults. But wearing his prejudices on his sleeve is not one of them. In fact, we all have prejudices; it's a good thing that we do; and we should admit to them.

By this I don't mean racial or gender prejudice but simply our pre-existing opinions. My prejudices, for example, include beliefs that: the efficient market hypothesis is mostly right at the micro level; we all are prone to countless cognitive biases; that neoliberalism has failed to stimulate growth; that greater equality of power and wealth would be a good thing; and so on.

Without such prejudices, our opinions would be unduly swayed by every fleeting voice we hear or data point we see. We'd be so open-minded that our brains would fall out.

In finance, a lack of prejudice produces noise (pdf) traders - people who mistake mere noise for solid information and so trade unnecessarily. Over time, this will lose them money. If such traders had the prejudice that profit opportunities were scarce they'd trade less and so markets would be more efficient.

A lack of prejudice can lead to illusions. There's a rare neurological condition in which sufferers believe that family members have been killed and replaced with replicas. A doctor was once talking to one such patient and asked: "isn't it unlikely that such a thing would have happened?" to which the patient replied: "Yes. I'd never have believed it if I hadn't seen it with my own eyes." A little more prejudice and a little less willingness to believe the evidence would have helped that man. I suspect the same is true for beliefs in conspiracies and the paranormal.

A lot of apparent evidence is weak. It can be noise rather than signal and even academic research is sometimes unreplicable (pdf). Given this, it's wise to cleave to our prejudice. Marvin Gaye had a point when he advised us to "believe half of what you see and none of what you hear."

By "prejudices" I do of course mean "Bayesian priors". And saying this alerts us to the real problem. It is not that we have prejudices or even flaunt them. It is that we fail to update them properly in light of the evidence. Racial prejudice survives, I believe, because of a failure to respond dispassionately to day-to-day evidence about what black people actually are: Liam Neeson's error was to fail to see that millions of black men had not raped his friend.

What I find unpleasant about Mr Humphrys is not so much that he wears his prejudices on his sleeve but that he seems too incurious to look for evidence that might disconfirm those prejudices. There's a big difference between saying "I think Brexit is a good idea: what is the evidence to the contrary?" (which I think would be tolerable in a BBC interviewer) and simply harrumphing over anybody trying to present such evidence whilst giving a free pass to those who support one's prejudice.

In this, of course, Mr H is not unusual. A lack of updating - Bayesian conservatism - is common even when people have incentives to avoid it: I suspect it accounts for at least some of the post-earnings announcement drift and momentum effects we see in stock markets. Worse still, there can be counter-updating, whereby disconfirming evidence causes us to actually strengthen our prejudices.

It's hard to fight these tendencies not to update properly: I've suggested ways to do so, but with no confidence that I follow my own advice.

Worse still, these tendencies are not merely psychological. They are social too. Most of us live in our own bubbles and associate with like-minded people, which leads us to reinforce our prejudice and to regard others as mere caricatures: there's a massive subfield of metropolitan journalism which portrays the white working class as ill-educated and backward. And commentmongers have little incentive to express the open-mindedness necessary for good updating: a willingness to admit you were wrong is not an obviously good career move.

The problem, then, is not prejudice. It's that there's a failure to update such prejudices and big psychological and social pressures upon us to stick to them.