Can 50%+1 of the voters use 'legislative democracy'(your word for initiative by simple majority vote) to overturn the right to keep and bear arms?
Can 50%+1 of the voters use 'legislative democracy' to give women the right to vote?
Can 50%+1 of the voters use 'legislative democracy' to make it legal to take property from anyone, whether an individual or some particularly defined group, such as illegal aliens?
Did your vote for the President of the United States directly count? Is your vote for the presidential candidate of your choice 100% certain to always be applied to the candidate of your choice? How much is your presidential vote worth, when compared to the 'worthiness' of voters in lightly populated states such as Wyoming or Idaho?
Can a President of the United States be elected with less than 50%+1 of the voters supporting him or her? Can the will of the people in a presidential election ever be overturned by judicial activism?
What if 50%+1 of the voters use 'legislative democracy' to make some aspect of what is fundamental to you (your particular religion, say,) illegal to practice? Will you just go, "Oh, well, guess I'd better do what the majority tell me to do"?