Plato republic question?

How is a liberal representative democracy different from the sort of direct participatory democracy Plato has in mind? How many, if any, of Plato’s criticism of the shortcoming of a direct participatory democracy are addressed in a liberal representative democracy and do any of his criticisms still apply to a liberal representative democracy? Take an historical example, past or contemporary, that you think exemplifies the tensions or disunity or unraveling that Plato describes in one of his degenerate states.