Voters can cast either 0 or 1 votes for each alternative. The alternative with the greatest number of votes is declared the winner. This method was independently proposed by several people in the 1970s. Since then, it has been adopted by various governments and organizations around the world, most notably by the United Nations to elect Secretary-General. Motions to adopt it have also been tabled in several states.
Approval voting does pass the Independence of Irrelevant Alternatives criterion.
It can't directly be evaluated using some of the other criteria listed above, however, since their statement is specific to preferential voting methods. However, various counter-intuitive situations can stil arise. For example, take the following preference ballots. Alternative b wins, and the dishonest voters have achieved a preferred outcome. Another problem is that the mapping from a voter preference ballot to a set of approved voters is poorly defined.