““The United States shall guarantee to every state in this union a republican form of government”
I regard legally binding ballot initiatives as unconstitutional.”
Having done an enormous amount of study and having written a book on republican government, I disagree with this point.
In simplest terms, a republic is rule by law (as opposed to rule by men, which monarchy, aristocracy and democracy are), where the laws are made by more than one person (an assembly of persons, thus a legislature).
In the case of a ballot initiative, the people themselves act as their own legislature, in that it is they who are making the law, instead of delegating their legislative power to representatives to make the law.
But the ballot initiative, in my opinion, is still republican since the resulting law applies to all.
But to your point, a ballot initiative is the closest thing to an actual democracy that we can see. For in a democracy, all the people gather in one place to vote (which never happens and is very unwieldy), and even then, the it is rule by majority over the minority, leading to tyranny. Whereas in a republic, even if the people make their own laws, the law apply to the majority AS WELL as the minority.
A lynch mob fits this definition.