Simpler is better => Everybody who wants to understand it, does understand it. Electoral college may have been the simplest viable system in its day, but modern rapid communication enables much simpler alternatives.
Self-evidently-fair => This is hard, because "fair" is subjective -- and there will be factions who claim _any_ system is rigged or biased. Despite the subjectivity, some systems are obviously fairer than others -- extreme example: simple majority voting is fairer than throwing the votes away and appointing a hereditary king. We can certainly come a lot closer to "objectively fair" than the current US presidential system, though. Electoral College system is self-evidently unfair despite its historical honorable intent. If you live in a rural-dominated state your vote counts more than if you live in an urban state. For that matter, if you live in a small (swing) state, your vote counts more than if you live in a large state. And, if you live in a non-swing state, your vote doesn't count at all!
Based on these criteria, my top two choices (in no particular order) would be:
- Popular vote, winner takes white house. (The clear winner of the "simpler is better" criterion).
- Popular vote with instant runoff system. (Still fairly simple. I won't bother describing it, it's pretty clear on Wikipedia).
Instant runoff handles "spoiler" candidates better IMO. (I say IMO, since "better" is of course subjective).
Instant runoff may even help discourage the de-facto two-party monopoly that exists fort the US presidency.
For these reasons I have a slight bias towards instant runoff, but still think either of the above variants of popular vote would be vastly better than what we have now.
BTW, does anybody reading this know where I can find the Douglas Hofstadter essay on voting systems? I read it years ago. He demonstrated the pros and cons of many different voting systems, and clearly showed by example that no voting system is perfect. As I recall, for each system he described a scenario that produced outcomes that satisfied none of the voters.