Provocative research. I have several thought about this.
First, was the meaning of "democracy" presumed or specified. If "democracy" is defined as "government of the people, by the people and for the people," then no nation today is living under democracy. Most liberal democracies are republics, which have been controlled by elites historically and this remains true today. Patricians are seldom much concerned about the interests of the plebeians other than with respect to getting their votes periodically in elections.
Secondly, if "democracy" is taken to mean "majority rule," then the United States is not a democracy, for several reasons. Most importantly, minorities are protected from the tyranny of the majority by constitutional rights and a judiciary as a check and balance on the legislative and executive powers.
In the US, the senate is comprised of two senators from each state regardless of size or population. This protects state sovereignty in a federation.
Less important — usually — is the role of the electoral college in balancing the interests of different demographic areas, chiefly the state with large urban populations and the states with large rural populations. But this becomes very important when the winner of most electoral votes does not carry a majority.
These aspects of liberal democracy result in some of the paradoxes of liberalism that result in dissatisfaction with political liberalism.
In addition, political liberalism must be harmonized with social and economic liberalism, which engenders further paradoxes of liberalism.
ht Jerry Lynn Scofield at Naked Capitalism