give everyone half a dozen votes or more, and and you'll get a more representative sample.
for example instead of electing a president, elect a while leadership team. independent of party affiliation. (i'd get rid of parties completely while we are at it, every candidate should be independent (the expanded version of that gets even rid of candidates, every adult can potentially be elected, but that is a more complex system that needs more elaboration))
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?