There’s a chasm between the will of the British people as expressed in their 52% vote for Brexit and their considered will. It turns out that ordinary Britons deliberating with their peers think things through, “unspinning” much of the surrounding media hysteria.

In late 2017, a group of universities selected 50 people by lot to be representative of ordinary Britons in a “citizens’ assembly”. Between the referendum and the end of two weekends spent deliberating on Brexit, a group exemplifying the referendum’s 52:48 Brexit vote had swung to 40:60 against.

The researchers claimed it “would be wrong to draw strong inferences”. They pointed out that only four participants had changed their minds over the two weekends. But that’s still an 8% swing in a population of 50. And it ignores three others who’d already swung away from Brexit between the referendum and the assembly’s commencement.

The tragedy of Brexit doesn’t concern Britain’s economy but rather its democracy

One of the researchers told me that no remainers changed their minds. So the chance of seven anti-Brexit changes of mind simply reflecting random chance are those of a coin landing heads-up seven times in a row – less than 1%. Moreover, a deliberative poll in 2010 delivered strikingly similar results. Asked, among a host of other questions, whether there should be a referendum on Brexit, support fell from 60% to 45% over the course of the deliberation, with the organisers estimating the probability of a referendum being one in 1,000.

These changes are part of a larger picture. As the citizens’ assembly considered the issues, the participants became more tolerant and generous towards each others’ perspectives, and more liberal in outlook. Participants became slightly more inclined to think immigration enriched rather than undermined cultural life and the economy, and substantially more prepared to give priority to trade over immigration in Brexit negotiations.

Q&A What is a hard Brexit? Show A hard Brexit would take Britain out of the EU’s single market and customs union and ends its obligations to respect the four freedoms, make big EU budget payments and accept the jurisdiction of the ECJ: what Brexiters mean by “taking back control” of Britain’s borders, laws and money. It would mean a return of trade tariffs, depending on what (if any) FTA was agreed. See our full Brexit phrasebook.

The endless cycle of trivialisation and polarisation – the hatred spewing daily from mainstream and social media – is a wicked problem that’s setting whole classes against each other. With a man-child now inhabiting the White House, how long till we realise we’re facing a diversity challenge of existential magnitude? The traditional diversity agenda regarding gender, ethnicity and race is important, but western democracies are being torn apart by the alienation from politics of losers in the race for income, education and social connections.

Intriguingly, the Ancient Greeks had a word for what’s missing: isegoria, which they thought must accompany freedom of speech, and which means equality of speech – people need to hear their own voices reflected in political discourse.

It’s a cliche that there are no magic bullets. But all the evidence suggests that involving ordinary citizens in democratic deliberation – as is becoming more common in Ireland, Canada and Oregon – can help us do democracy so much better.

Party politicians shy away from bold action on many of the great problems of our time – from obesity to drug and welfare dependence – for fear of their efforts being publicly misrepresented by well-funded interests deploying the usual dark arts, with the media desperate for eyeballs.

On Brexit, citizens’ juries could become citizen activism. With less than £2m – from philanthropists and crowdfunding – we could host at least 10 citizens’ juries, each chosen by lot from their local communities around Britain, to be held simultaneously over two weekends and overseen by a board of respected citizens of diverse political views.

We should also find the funds to establish a standing citizens’ assembly of between 200 and 300 ordinary Britons to shadow the Brexit negotiations so that the considered opinion of the people remains a beacon throughout. Non-government parties could strike a blow for democratic renewal as well as ingratiating themselves with the public by seeking funds to do so from the public exchequer. Experience suggests that involving ordinary citizens like this is a real vote winner.

Then we might ask the same body for its considered advice on other matters.

The tragedy of Brexit doesn’t concern Britain’s economy but rather its democracy. If the way British democracy comports itself in responding to the referendum doesn’t change, half its population will forever resent the outcome as illegitimate, and add it to their other, growing resentments.

By borrowing from the practice around which ancient Athens founded democracy – the involvement of ordinary citizens deliberating among their peers – we could transform Britain’s slow-motion agony into a triumph in which democracy was renewed to embody not just the will of the people, but the safer, more practical and generous notion of their considered will.

• Nicholas Gruen is chief executive of Lateral Economics and chairman of the Australian Centre for Social Innovation