Why are democracy and liberalism correlated?

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?