In the central marketplace of ancient Athens, around 350BC, there stood a machine called the kleroterion. This was a six-foot-high slab of stone that had a series of slots on the front, and a long tube bored down from the top to the base. Those up for selection for the various offices of state would insert metal ID tags, called pinakia, into the slots, and a functionary would pour a bucket of coloured balls, suitably shaken, into the top of the tube. The order in which the balls emerged would determine who took which role, some for the day, some for a year.

Today the kleroterion survives, in fragments, in Athens’ Museum of the Ancient Agora, alongside other pieces of democratic technology such as the clepsydra, a water clock used to time orators’ speeches and the fragments of pottery, called ostraka, on which they scratched the names of the too-powerful politicans they wished to see banished from the city, and from which we derive the modern word “ostracism”.

The method of governance embodied in the kleroterion, which dates back to the very establishment of democracy, is called sortition, meaning selection by lot, as opposed to election by vote. The Athenians believed that the principle of sortition was critical to democracy. Aristotle declared that: “It is accepted as democratic when public offices are allocated by lot; and as oligarchic when they are filled by election.” But along the way, sortition – and the even more exciting possibility of actual banishment – has fallen out of most democracies’ toolkits.

Sortition in ancient Athens had a number of important qualities. First, those eligible for selection included the entire suffrage (which, it must be noted, was at the time limited to adult male citizens). Second, it applied to much more than jury selection, which is the only form in which sortition survives in most places today, and included magistrates, legislators and the main governing councils of the city – all the important posts, in fact, bar the military. And third, and perhaps most significantly, it both embodied and enabled transparent and participatory governance: that is, anybody could come down to the agora and not merely see but understand how the machine worked – and anyone could be selected by it.

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Sortition has received an increasing amount of attention in recent years, as we seek alternatives to our creaking, gerrymandered and short-sighted electoral processes. The kind of citizens’ assembly called for recently by a number of public figures in the service of breaking the Brexit deadlock has its roots in sortition, involving members of the public, selected at random. This form of assembly has been employed in a number of other countries, most notably in Ireland, which created a citizens’ assembly in 2016 to consider a number of questions. The Irish version consists of 99 complete strangers, selected at random from the electoral roll, who meet over a series of weekends to learn about, debate and vote on contentious issues, such as abortion rights and climate change. And already, the results have been surprising: the citizens’ assembly has been credited with providing the momentum for the legalisation of abortion, and recently voted overwhelmingly for a series of measures to cut greenhouse emissions that politicians had dismissed as unworkable.

Some fascinating psychological research underlies the subversive possibilities of sortition, which is best summed up by the phrase “diversity trumps ability”. This is the theory that solutions to knotty problems are best found by starting from the greatest number of different viewpoints and experiences – that is, from as wide a selection of people as possible. The cognitive diversity of such a group – which is not the same as racial or gender diversity, but is highly correlated with it – leads it to different and potentially more effective solutions. This is notably counter to the belief, dominant in electoral systems, that there exists a mythical best person for the job, capable of engaging with any number of different areas of policy. It has been found in multiple studies that random selection from a large group produces better answers to complex problems than the appointment of a narrow group of experts, making sortition a quite revolutionary idea if we choose to take it seriously.

Citizens’ assemblies do away with elections, lessening the pressure to vote a particular way, and thus improving the quality of decisions made, particularly when it comes to difficult questions such as addressing the long-term effects of climate change – or leaving the European Union. They also provide a rare opportunity these days: for the citizenry to hear directly from experts in the field, to educate themselves properly about real issues, and then to take on the responsibility of decision-making for themselves.

The 99 strangers who proposed radical alternatives to existing political positions in Ireland did not start out as a homogeneous group. The assembly – randomly selected from the entire population, and thus truly representative of it – included those who were anti-abortion, pro-abortion and undecided; those who were fierce advocates for climate-change legislation, and those who rejected the scientific consensus. Yet through a careful and deliberate process of education and debate, it was possible not merely to reach consensus, but also to change minds: to progress, together, towards workable and even radical solutions. Citizens’ assemblies carry the whiff of populism, but they are the opposite of strongman politics. By providing transparency and participation, they are an opportunity for people to actually engage with the messy business of politics, rather than shout and wave flags from the sidelines.

In this, they have something of the kleroterion about them. It’s easy to forget in these days of obfuscatory and complex technologies, of electoral manipulation by hackers and bots, and when most of the government is having a conversation with itself via broadcast and social media – which is inherently oppositional and destructive – that the technologies of political process can also be tuned to transparency, accountability, understanding and education. And yet the possibility exists as clearly in the citizens’ assembly as it did in ancient Athens.

We spend our days hoping that somebody, anybody, will come up with solutions to the issues we face; but nobody is coming to save us. There is no appeal to a higher power here. We have to build our own alternatives – and that really does mean all of us, from those on opposing sides to those who have had little or no political voice or representation until now. (In ancient Athens, as previously noted, the suffrage was limited to adult male citizens, and looking at the current make-up of parliament and corporate boards it doesn’t feel like we’ve actually improved that much. Real change will look very different; the optics are just a start.)

It’s clear that the blunt instrument of referendums and the sclerotic, corrupt framework of party and electoral politics have contributed greatly to the mess that we find ourselves in today. It is equally evident that viable alternatives exist, and their signal qualities are clear: diversity of representation (produced effectively by sortition), collective education and true participation in the democratic process, which involves not merely having one’s voice heard, but listening to others too. After all, the word “idiot” derives ultimately from the ancient Greek for “private citizen” – that is, one who has no interest in politics, and fails to engage meaningfully with their fellow citizens. We cannot continue to pretend we do not have the means to do better.

• James Bridle is the author of New Dark Age: Technology and the End of the Future