> Approval voting has the best balance between simplicity, fairness, and certainty.

Approval voting is completely inappropriate for common situations in Europe, where you have center-right, center-left, far-right and far-left candidate (e.g. presidental elections in France). Reasonable people should approve both center candidates despite of strong political disagreement with the other side (but still beter than fascists or communists). That essetially eliminates information from them entering to voting (although finding balance between right and left is one of the most important aspect of elections).

But that assumes people would hold common good strategy and not defect to vote only for their preferred candidate (while risking that extermists win). As the side who first defects wins, it is likely that it will just degrade to plurality voting.