I don't think anybody seriously thinks democracy is perfect or solves every situation. You don't need half baked "thought experiments" for that - there are real world examples out there.
"Democracy is the worst form of government - except for all the rest".
Representative democracies, of course, are not mob-rule.
But even if they were, generally the opinion of the mass is less bad than the opinion of a self-appointed individual or military-appointed individual.
Ebia, please correct me if I'm wrong about what I'm going to tell you in a paragraph or two to follow, because I haven't thought deeply about what about to say. Even I had reflected that way on it, I would still need your help.
Although I would prefer to live in Monaco partly because it's a Catholic principality, the US and state governments are the only ones I may already know well. Naturally, here in the States, we aren't living under mob rule. But we are, in my opinion, putting up with a federal government where congresspeople, our president, and others care too, too little about the common good. Their concern shortage helps explain why abortion on demand is legal here, why three or more states allow same-sex "marriage," and why members of Congress passed Obamacare when hardly anyone in Washington understood that roughly 2,300-page bill.
From what I can tell, American self-rule is probably an illusion. Even if it's genuine, I still have big problems with it. What we're suffering from here, I suspect, is a group of politicians who value their agendas much more than they care about the common good. Too often, they get their way when we the American people only think we're getting ours. Whatever falls into our national lap, we are, in Lockean style, supposed to endure it because we at least implied that we agreed to it.
You live in the United Kingdom, right? If you do, please consider yourself blessed because Her Majesty reigns as a nonpartisan sovereign who does care deeply about tradition, national unity, the common good, and the Holy Trinity's rights. England and the rest of the UK may be a largely secular place. The Queen may have much less power than I would want her to possess. Here in the United States, we're governed by a man who tries seemingly to use much more power than our Constitution supposedly grants him. However admirable his intentions might be, something I have no way to tell, his administration has been thoroughly destructive, in part, I suspect, because the United States allows something that pre-Vatican-II popes condemned long ago, the national government's refusal to acknowledge the social reign of Christ the King. For the Catholic Church God the Son deserves to rule much more than every Christian heart. Each government should apply His principles because He and the other divine Persons invented the universe, each part of it, and government as it is in itself. A government's legitimacy comes from the Father, the Son, and the Holy Ghost, not from the consent of the governed. As a pope asked, if a people governs itself, what happens to authority?
We in the United States, we as a nation, have denied Him what each nation owes Him, public acknowledgement of His inalienable rule the world and each nation in it. A country such as the one with it deistic Masonic origin pays pays God lip service while it prefers its will to His. If Her Majesty is a fine a person as she seems, I doubt that she approves of the way this country or its government treats God and His holy wishes. Many Americans call this country Christian one. I don't. A truly Christian one would let Christ and His holy Gospel affect everything that country did.
Like Sir Charles Coulombe, I'm a monarchist mostly because I'm a Catholic. I'm a Catholic first and an American second. I'm also a throne-and-altar conservative. Sadly, if American principles were the only American things I could conserve, there would be little or nothing for me to defend. Someday, if you happen to talk with Her Majesty, please tell her that you've met an American who believes firmly that the American Revolutionaries were traitors.
Although deliberative democracy may be impractical during a national election, I suppose, there's something good about it, too. Since voters talk about and debate what they'll vote, reasoning and evidence may help some voters vote for, say, the best candidate on the ballot.
