A democracy does not rest on the rule of law. A democracy is rule by majority where an individual, and any group of individuals composing any minority, have no protection against the power of the majority. We see this now as the Democrat majority in the House of Representatives are attempting to remove the president of the United States.
It is our republic that rests on the rule of law, i.e. the U.S. Constitution. Our republic is supposed to protects all its citizens. It was the reason the U.S. Senate had a supermajority rule until a Democrat changed the rule. It is the reason we choose a president with the Electoral College where the votes from all 50 states make the choice.