I particularly like the Swiss solution: employ topical referenda, and stop insisting that "everyone should vote". I'd rather have 60% of the people abstaining to vote because they don't care or don't know, than having them "sell" their vote to the lowest bidder with the nicest tie.

Especially for a "master of puppets"/figurehead election like POTUS, the problem isn't "too many uninformed people", it's "too many topics in a single vote". Even assuming 90% of your voters are knowledgeable about 90% of the issues, they can't express any of their knowledge in that single button or pencil stroke.

The same is true for trying to "divine" meaning to the votes cast, as well: since every voter only expressed a single button press, it's easy to dismiss votes that don't align with your own views as uninformed.

You want elections with depth? Don't make voting mandatory (either socially or legally), and use topical voting instead of figurehead voting.