Voters control the government in a liberal democracy. Under socialism, it is the sort of oligarchs whom you admire that control everything. Some of those voters in a liberal democracy happen to be industrialists, media moghuls, investors, and the like.
There are only evil people in charge under socialism. There are all sorts mucking about in a liberal democracy.
There is no such thing as a 'liberal' democracy. There is only democracy, or there is not.
There currently are no democracies in the world today. Not surprising, as it's an unstable form of government.