It's not enough to say that modern democracies don't descend from Athenian democracy. Modern democracies were deliberately designed to be unlike Athenian democracy. As a result, not a single modern democratic institution has a clear and direct Athenian ancestor. Our understanding of the word and the political system it describes is totally different.

The history of democracy as an idea is long and complicated and I can't do it justice here. The main thing I can do is recommend Jennifer T. Roberts' Athens on Trial (1994), which lays out the uninterrupted two-thousand-year anti-democratic tradition in Western political thought. It's pretty incredible to us from our modern perspective, in which democracy is considered an absolute good, but for most of recorded history it was universally regarded as a nearly absolute evil. The form of goverment we've ended up calling democracy was initially designed to be nothing like democracy, and its pioneer (the US) wasn't actually called a "democracy" until about half a century after its foundation.

So what happened?

To cut the ancient part of the story short, Athenian-style demokratia ("people power") slowly disappeared from the Mediterranean world after Rome rose to supreme power. From above, Roman authorities didn't like to deal with amorphous and unpredictable democratic governments, and instead encouraged their subjects to form local governments of single rulers or narrow oligarchies which were more easily connected to the Roman elite through personal ties of family and patronage. From below, political influence became less interesting as subjection to Rome removed the ability of states to formulate their own foreign policy or stand up for their own autonomy; the common people became more inclined to leave the day-to-day management to wealthy elites who rewarded them for their positions of power with lavish games, festivals and construction projects.

With actual examples mostly extinct by the start of our era, the only thing that remained of democracy was its rhetoric (with Roman emperors perversely claiming that they had founded the ultimate democracy because everyone was equal under their rule) and the literature produced in Classical Athens. But this literature was overwhelmingly negative about democracy. It was written by elites whose positions of power were threatened by the political equality and the supremacy of the Assembly that characterised democracy. People who read about Athenian democracy in authors like Thucydides, Plato and Aristotle - required reading for educated Romans - would come away thinking it had been a pretty bad idea.

Throughout the Middle Ages and the Early Modern period, the main Greek sources that European elites used to shape their thinking on democracy were Aristotle's Politics and Plutarch's Life of Phokion. These texts deliberately sketched democracy as an aberration: a cruel perversion of good government that resulted when the people were given too much power. They presented democracy as fickle, violent, stupid, petty, tyrannical and vindictive - mob rule at its worst, and with a frightening tendency to murder its own best guides and commanders. They overemphasised the infamous crimes of the Athenian democracy: the exile or execution of figures like Aristeides and Themistokles and Alkibiades and Sokrates and Phokion, the Arginousai trial, the razing of Skione and Melos, and so on. Other sources, including major authorities like Cicero, filled in the picture of a lawless city failing through its own untamed greed and lack of judgment.

This was therefore how the authors of the Renaissance and Enlightenment understood democracy. They may have recognised Athens' great achievements in art, philosophy and oratory, but they saw its political system as a dire warning against giving power to the people. In terms of political thought, their great models were Sparta and Republican Rome: places where the constitution combined elements of democracy, oligarchy and monarchy, and where the reckless will of the people was tempered (read: neutered) by reliable institutions dominated by the better classes.

The new political system that emerged in the 17th and 18th centuries and ended up as the model for parliamentary government worldwide was forged from this mindset. It wasn't intended to be an inclusive democracy; on the contrary, it was meant to protect individuals from the state and prevent countries from sliding into democracy. The Founding Fathers were terrified of democracy. To ensure that the common people wouldn't get their uncultured hands on public policy (or private property), a system of representative rule was devised, in which the true power would lie with members of the elite who received a mandate from their voters. To keep the riffraff even further from power, early representative governments maintained a property threshold for the right to vote. These two elements - election of magistrates, property requirement for full political rights - are listed by Aristotle as the defining characteristics of oligarchy. It may have been a more democratic system (in the modern sense) than any political system that had existed for more than a thousand years, but it wasn't democracy, and actively tried not to be.

There are complicated reasons why we've nevertheless ended up referring to this system as "democracy". In part, it was to do with a general rehabilitation of Classical Athens that began with the work of the ancient historian George Grote in the 1840s. In part, it was to do with the fact that the American experiment seemed to be working; Alexis de Tocqueville's Democracy in America (1835) did much to spread the idea that the system they had introduced had a positive effect on their citizens. Under the influence of works like his, the word began to change its meaning from direct to representative government, allowing its nature and value to be redefined. In part, too, it was because liberal elites in the UK and elsewhere genuinely started to believe that more people deserved a voice in government, even if their proposals were modest at first. There was a growing sense that only representative democracy could guarantee individual rights, private property, freedom of speech, and other political values that had only recently been articulated. Finally, all of these reasons were cemented during the World Wars, when countries like the UK and the US could more or less rightly claim to represent (parliamentary) democracy against the absolutism or totalitarian despotism of their enemies.

In other words, ancient and modern democracy are almost entirely disconnected political concepts. The word simply doesn't mean the same thing in each case. There is no direct line between the two. Instead, ancient democracy went extinct during the Roman Empire and never reemerged. What we have now is a new political system, mixing idealisation of the Roman Republic with new Enlightenment political ideas - a system that, for all its rhetoric, wouldn't look the slightest bit democratic to the Ancient Greeks.