It's like on the Apollo missions where some parts were made by two completely different manufacturers and worked completely differently.
Hybrid political systems are best. Of course if we like democracy (and most people do), then that should be the most common kind of component. But I'd still like to have some different paradigms mixed into the system. And that's exactly what most modern constitutions do, for better or for worse.
Maybe also a 3rd chamber, where the weight of your vote was proportional to IQ (much more palatable in EU than US).
Why exclude teachers from picking the education minister? If we're restricting votes, shouldn't they be the only ones doing so instead?