I'm not sure what sort of mechanism you're thinking of. My example has a majority preferring X & Y over ~X & ~Y, but with simultaneous majorities preferring ~X

I'm not sure what sort of mechanism you're thinking of. My example has a majority preferring X & Y over ~X & ~Y, but with simultaneous majorities preferring ~X over X and ~Y over Y. This is fundamentally tricky to resolve. And furthermore, the power to propose "X & Y" is incredibly useful, since you get to shape the negotiation options for compromises. Even with a direct democracy system, you'd still want to be able to vote in or out some kind of elected representative for proposing various bills.