At first, it might be difficult to believe that a non-rank method could be one of the best, that it could be better than nearly all rank methods. So I'm going to briefly discuss Approval in use.
Sure, Approval needs strategy, as does IRV. Some of the criteria in the Approval article compare those 2 methods strategically. Approval's strategy is nothing new: Vote for the same candidate for whom you'd vote in 1-vote Plurality--and also vote for everyone whom you like better than him/her.
For simplicity, say there are 3 candidates: Favorite, Middle, & Worst. If you don't think Favorite can win, then of course you should vote for Middle in addition to Favorite. Now, someone might object that Favorite could have a win, and, not knowing that, you might vote for Middle, and give the election away to him/her. Sure, but this is different from Plurality because with Approval, voting for both, you aren't voting Middle over Favorite, as you'd have to with Plurality, and often with IRV. You merely aren't voting a preference between those 2 candidates. And so, with Approval, as compared to Plurality & IRV, it takes twice as many' mistaken compromisers to give away the election.
Obviously, if Favorite's voters are a majority, then they should vote only for Favorite. Obviously, if Worst will get more votes than Favorite, then Favorite's voters should vote for Middle in addition to Favorite. But please note that being mistaken about whether Favorite has a majority, or has fewer votes than Worst, would usually be a _big_ mis-estimate, a big case of wrong information. Let's not exaggerate the likelihood of a mis-estimate of that magnitude.
Say that Worst's voters feel sure that Worst will get more votes than Favorite, and so they don't help Middle, because they don't need to. Well it's reasonable that the Favorite voters would know that too, and would know to help Middle, whom they need. It's reasonable to assume that all the voters have access to the same information.
But suppose that everyone believes that favorite will get more votes than Worst, and the reverse turns out to be true. No problem. Worst's voters, believing that Worst will get fewer votes than Favorite, will vote for Middle, who will then get at least as many votes as he/she would have gotten had Favorite's voters voted for him/her.
The point of the above paragraphs is that Approval's strategy choices aren't the problem that some might claim them to be.
I liken Approval to a solid, reliable handtool. You're better off with that than with an automatic power tool that will often go haywire and do unintended things--as rank methods will, except for a very few of the very best, the versions of Condorcet's method.
As the criteria in the Approval article show, Approval is the most stable single-winner voting system. Uniquely stable, and elegantly simple.
In conclusion, I'd like to answer one more criticism of Approval that frequently comes from IRV advocates. It's heard so frequently that I devote the next 3 paragraphs to it:
Advocates of IRV sometimes say that in Approval your vote for your 2nd choice counts against your 1st choice. As I said, when you vote for both, you aren't voting 2nd choice over favorite; you merely aren't expressing a preference between those 2, because you'd rather vote both of them over someone you like less. IRV advocates say that with their method your 2nd choice vote can't hurt your favorite--no, because before IRV lets you help your 2nd choice, it eliminates your favorite. It saves your favorite by eliminating him/her. A sort of electoral euthanasia.
Suppose we define a method that's the same as Plurality, except that you can indicate your 2nd choice, and it won't be counted. Of course that 2nd choice vote can't count against your favorite. That's what we have with IRV, except that your vote for 2nd choice over last choice may or may not be counted.
Additionally, if, in IRV, you help your 2nd choice by insincerely ranking him/her in 1st place, as IRV will often strategically force you to do in order to prevent the election of your last choice, then that kind of help for your 2nd choice will often defeat your favorite when you do it mistakenly, when your favorite had a win. If you say that can happen with Approval, then I repeat that Approval requires twice as many mistaken compromisers to give away an election compared to IRV or Plurality.