> Approval voting is cheap and easy to implement, dead simple to explain, count, and audit.

Not so dead simple to vote, though. If you're a sincere voter and you prefer Alice to Bob and Bob to Charlie, do you approve of Alice, or both Alice and Bob?

That choice has to be either strategic or very noisy.

There seems to be some unavoidable complexity to voting methods: letting the voter deal with the complexity leads to a method with a very simple algorithm but that's tricky to use. Letting the method itself deal with it leads to more complex algorithms, but makes it easier to vote.

That said, the alternative vote is a bad ranked voting method; with that I do agree. Just beware of the complexity hidden in the system, whether that's Approval or Ranked Pairs.