This week, a judge at Blackfriars Crown Court in London ruled that a Muslim woman can wear the veil, or niqab, in court, but must remove it when giving evidence.

Some immediately said he should have gone further. For instance, the redoubtable Janice Turner of The Times declared on Twitter that the decision makes “an awful precedent”. She argued that being able to observe a person is important when coming to a decision about their guilt. Janice’s views echoed those of the National Secular Society, which told the BBC it’s “vital” that defendants’ faces are visible “at all times”. In other words, veils should be banned from court, tout court.

I agree that the judge’s compromise is unsatisfactory, and I too would like to go further, but in the opposite direction. I think we’d have a better justice system if all witnesses were made to wear a veil.

In the course of researching my book Born Liars, I spent a lot of time reading the academic literature on lie detection, and talking to scientists who study interrogation techniques. I found a surprising scientific consensus: people are less good than they think they are at judging a person’s truthfulness by observing their demeanour. Humans, it turns out, make erratic lie detectors. But here’s the funny thing: we think we’re great at it.

In a landmark study from 2006, the researchers Charles Bond and Bella DePaulo asked 2,520 adults in sixty-three countries how to spot a liar. Most people confidently explained that liars stutter, squirm and avert their gaze. The same preconception persisted in every culture studied. The trouble is, it’s not accurate. As a result, it leads us astray.

A person telling a lie may look their interlocutor in the eye. They may well – especially if they have had time to prepare – be just as fluent, if not more so, than a truth-teller. Conversely, some people, even when they’re telling the truth, appear shifty and uncomfortable, especially under pressure.

We’ve all encountered successful liars. So why, Shakespeare’s warning notwithstanding, do we continue to believe that we can “find the mind’s construction in the face”? Emily Pronin, a psychologist at Princeton University, points to a fundamental imbalance in the way people relate to each other.

When you physically encounter me, there are two things that are more prominent in your mind than in mine: my face and your thoughts. As a result you give too much credence to what you think you can tell from my face, while remaining confident that your own thoughts are entirely private.

Studies have found that people consistently over-estimate how much they can learn about others in job interviews, while at the same time believing that others can get only an unreliable glimpse of what they’re thinking or feeling. The model we work with is something like this: I am never quite what I seem; you are an open book. Pronin calls it “the illusion of asymmetric insight”.

It’s an illusion that sits at the heart of our justice system. The lawyer and fraud specialist Robert Hunter, whom I interviewed for the book, calls it “the demeanour assumption”: this assumption that we can read others’ faces like a book. Hunter believes that the demeanour assumption regularly misleads interrogators, judges and juries.

When a jury is trying to come to a decision, they need to take all sorts of information into account. What a witness is doing with their face while talking is, to a large extent, noise in the data, a hindrance to the search for truth. In their study, Bond and DePaulo found that “people are more accurate in judging audible than visible lies”.

Critics of the veil like to refer to the long traditions of our justice system. But if niqab-wearing women make us pay attention to this flaw in the system for the first time, isn’t that a good thing?

We can stop witnesses wearing veils. Or we can make all witnesses wear them. Either way, let’s not pretend that banning the veil in court will lead to better justice.