We don't need a "new theory of democracy" - we need to actually follow the Constitution we already have.
The author's concerns about majority rule leading to bad outcomes? That's exactly why the founders created a constitutional republic, not a pure democracy. They knew about mob rule and designed safeguards against it.
The Constitution already handles these problems:
Contradictory voting patterns: Federalism lets states make their own choices. If Kentucky votes against Medicaid expansion, that's their call - other states can do differently and we can all see what works.
Demagogues: Separation of powers stops any president from becoming a dictator. Congress controls spending, courts check unconstitutional acts, and the First Amendment protects counter-speech.
Protecting rights: The Bill of Rights and 14th Amendment protect individuals even when majorities disagree.
Rather than throwing out 250 years of constitutional law, maybe we should just enforce what we have? The framework works when we actually use it. The real problem isn't that democracy has "failed" - it's that we've stopped following our own rules.