For the purposes of this question, let me (loosely) define:
Democracy = situation where the government is chosen by the population (using some ‘reasonable’ voting rule)
Liberal state = state which allows individuals to make their own personal choices (e.g. what religion to follow, how to dress, what sexual practices to engage in, etc.)
Notice that, for the purposes of this question, I am not bundling democracy into the definition of a liberal state. Moreover, we can easily imagine a state that is highly liberal (on my definition) but autocratic.
Empirically, there seems to be a strong (positive) correlation between liberalism (as defined here) and democracy. [Equivalently, there is a correlation between illiberalism and autocracy.] Question: what explains this correlation?
Of course, one can think of various answers to this, e.g.
People like liberal freedoms; people tend to get what they want more in democracies (than in autocracies); so democracies have more liberal freedoms
For democracies to be stable, election results need to be accepted even by those who voted for the losing side. This is much harder in an illiberal state since the consequences of having a government that you don’t like are much more severe.
Is there a ‘canonical’ explanation favoured by the political scientists who have thought about this?