The ideal aristocracy declines when its guardians begin to value honour over wisdom, producing timocracy — the rule of the ambitious, exemplified by Sparta. The timocrat's son, watching his father humiliated by the pursuit of honour, turns toward wealth instead: oligarchy emerges. But the oligarchic city is divided between rich and poor, and the poor eventually overwhelm the rich: democracy is born.
In the democratic city, every appetite is treated as equal to every other. Liberty becomes licence; discipline is condemned as servitude. The children of the demos grow up ungoverned by reason or authority. Freedom, pushed to its extreme, destroys itself — preparing the ground for tyranny.
The tyrant emerges from the most ungoverned democratic souls: enslaved to a single monstrous passion, he destroys friendship, corrupts law, and can trust no one. He appears most powerful and most free — and is in reality most wretched. The sequence ends not in strength but in the most abject servitude: the city enslaved to a man who is himself enslaved to desire.
Each constitutional type maps directly onto a psychological type. Plato's insistence is that politics is psychology writ large: the kind of city a people builds is the kind of soul they collectively possess. If you want to understand a city's vices, look at the vices its citizens most admire.
The five-constitution sequence appears in Books VIII–IX of The Republic. Plato's analysis of democratic licence anticipating tyranny has been cited in debates about Weimar Germany and other democratic collapses.