Approval voting does not meet the following criteria:
- Majority: if a majority of voters prefer one candidate to every other candidate, does that candidate win?
- Majority loser: if a majority of voters prefer every other candidate over one candidate, does that candidate lose?
- Mutual majority: if a majority of voters prefer every member of a group of candidates to all candidates not in the group, does a member of that group win?
- Condorcet: if there is a unique Condorcet winner, does that candidate win?
- Condorcet loser: are Condorcet losers guaranteed to lose?
- Smith and ISDA.
- Later no harm. If I add a candidate to my ballot, is that guaranteed not to make a more favored ballot lose?
Later-no-harm and Condorcet are incompatible, so no voting method supports both. But many voting methods manage one or the other.
You can use the same voting machines and ballots
Ballots sure. I'm not convinced on voting machines. But I'm also not convinced that using the same ballots is a good idea. What if people don't realize that they are supposed to change how they vote and only approve one candidate. Then it devolves into plurality voting.
It never requires more than one round of voting
But that means that voters are choosing among a large number of similar alternatives. Two rounds of voting mean that people who don't know who to choose in the first round can still participate in the second.
It avoids spoilers and reduces the opportunity for strategic voting
It fails later-no-harm, so there are spoilers and strategic voting.
The suggested way to do approval voting is to either order all of the candidates and pick those you prefer more than you wish to avoid or to pick a pivot and compare the rest to that person. If you're ordering all the candidates, you might as well do ranked voting. And choosing a pivot is definitely strategy.
The biggest problem that I have with it is that it doesn't allow me to say that I prefer one candidate to another except in the approval. So I can basically say that I prefer one group of candidates to another group. But I only get two groups. I would rather use one of the more complicated ranked voting methods as better expressing my actual preferences.