I'm not a big fan of democracy. However, I believe that referenda are a truer form of democracy than just about anything else in the world today, so if you're a support of democracy you should find it difficult to argue against them.
When used in a hybrid model (as in most of the places that allow them), where a legislature handles most legislation but that the public is occasionally allowed to introduce and vote on additional policy, you might get the best of both worlds. Parliament or whatever you call it can handle most of the boring day-to-day legislation, but anything that the public is moved to act upon and for which parliament is refusing to conform to popular opinion can be changed without politicians being able to cheat that.
This isn't a subversion, but an improvement.
That said, I think democracy is unsalvageably bad and should be abolished. Officeholders should be selected by lottery, with everyone eligible to run for office having an equal chance of winning. No more parties, no more incumbents. For those positions where there is a single point of failure (US president, for instance), these could be expanded enough (a triumvirate) that the bad luck of selecting some insane citizen need not result in nuclear armageddon.
This would eliminate all voting, and thus, all democracy. And yet it would preserve the aspects of modern democracies that people seem to like best. Quite frankly, you're all bad at voting. We all are. It's impossible to develop a voting strategy that can achieve any aims that any sane person should want to achieve. Let's just get rid of it.