What if all governments were liberal democracies?

Plato didn't have a very high opinion of democratic government, of course. Athenian democracy was crushed by Spartan autocracy, because, ultimately, the autocracy was more rational in its goals than the democracy. Ordinary people aren't particularly rational or realistic in their goals, so, why should governments elected by them be expected to be competent? Winston Churchill described democracy as "The worst form of government, with the exception of all other forms of government." Was he right? Certainly, a great many Western historians attempt to make the case that all totalitarian, autocratic systems of government are terribly repressive and destructive. And, frequently they are, of course. On the other hand, a truly capable and reasonable dictator -- Julius Caesar, for example -- can frequently achieve more, and help people more than any elected, Parliamentary body is likely to be able to do. Of course, an incompetent dictator can do incredible damage, and, they often do. So, what if all governments were liberal democracies? What would the world be like, exactly? How would it differ from our own world?