That's why we have nowadays Republics, with either written constitutions or fundamental legal texts like Habeas Corpus, not just pure democracies à la antique Athens.
The way out of your conundrum is to admit there is no "the People"; there is a collection of diverging, often incoherent trends, and no voting system is perfect (no voting system is even logical, as proven by Condorcet and Arrow[0])
Arrow is not at all "procedural", the French know it well: the 1995 presidential election ended with a Chirac vs Le Pen (the patriarch) duel, even though Lionel Jospin was the favorite and would have beaten both if he had faced them off... A clear example of non-transitivity in elections.
That's my point, sorry if it wasn't clear. Non-transitivity is resolved procedurally. We can theorize about Arrow all we want; in the meantime we can write rules that actually do produce electoral results.
My point is that it wasn't resolved: Jospin was the favorite, but the French were forced to choose between two candidates the majority of them loathed. The rules were a failure.
The way out of your conundrum is to admit there is no "the People"; there is a collection of diverging, often incoherent trends, and no voting system is perfect (no voting system is even logical, as proven by Condorcet and Arrow[0])
[0] https://www.investopedia.com/terms/a/arrows-impossibility-th...