It's interesting to consider which US elections would have had a different outcome with approval voting. Certainly the 2000 election. People could have voted both for Nader and Gore, which would have tipped Gore over the edge.

How about 1992? Could Bush have won if angry republicans would have a chance to vent their anger by also voting for Perot? Or might Perot have won since voting for a 3rd party candidate wouldn't feel like a lost vote.

To demonstrate the problem with approval voting (all voting systems have problems, as was proven by Kenneth Arrow in 1951): if Obama, Clinton and McCain would all run, McCain would probably win, even if a majority of voters preferred either Democrat.

So, approval voting should allow fair elections with more than two candidates, but in practice it doesn't, because people vote strategically.