Liberalism states that we must be self-determining to be fully human (hence "autonomous"). Therefore, the first phase of political modernism was devoted to abolishing non-contractual forms of political power. The power of kings and priests was held to be illegitimate because it did not involve an act of consent from the governed.
And so we ended up with "liberal democracy". However, there's a problem. Democracy might seem to fit in with autonomy theory as it involves a formal act of consent. But what if a democratic majority chooses goods other than the maximisation of liberal autonomy? What are liberals to do then? Do they continue to support democracy, as a political form based on consent? Or do they oppose it as bringing about outcomes which conflict with liberal first principles?
Geoff Robinson, an Australian labour historian, has discussed this quandary for liberals like himself in a recent blog post Democracy vs liberalism? He recognises that majority opinion often runs against liberal political aims. He mentions the Tampa incident of 2001 when 77% supported turning back the Tampa, a ship carrying illegal immigrants to Australia; Lipset's theory of "working-class authoritarianism" in the US; and the "populist conservatism" which has "challenged the American left in its heartlands".
So how does Robinson seek a way out of the contradiction? Does he support democracy even if this leads to non-liberal majorities? Or does he seek to preserve liberal first principles against democracy?
He takes the latter option. He reminds us that the first principle he holds to is that of autonomy (fulfilling our potential through self-government). He then writes that:
We are not obliged to support capitalist democracy when it reduces the ability of humans to fulfil their full potential. Democracy, as James Bryce noted long ago, has won support as a means to an end ... We cannot be 'all for' democracy as currently constituted.
This, though, isn't really a solution to the contradiction. It is merely an assertion of which contradictory option he prefers. After all, preserving "autonomy" from non-liberal democratic majorities means abandoning "autonomy" in terms of democratic consent as a basis for political power.