Among ranked voting methods, ranked pairs seems most compelling to me.

I think that’d fail miserably in the real world.

Think about the average voter. They see this ballot:

A vs B?

A vs C?

A vs D?

B vs C?

B vs D?

C vs D?

Yea I think they’re gonna freak out upon seeing this ballot. Right now, the most important goal should be to get rid of the spoiler effect and FPTP, rather than finding the best system.

approval seems pretty good (and extremely simple).

I can see a bit of strategic voting happening.

Let me demonstrate:

For the sake of simplicity, let’s say we have 3 candidates, and no term limits:

Trump, Biden, Sanders

Biden and Sander voters dispise trump, their preference in RCV is (example):

Biden>Sanders>Trump: 30%
Sander>Biden>Trump: 25%
Trump>Sanders>Biden: 23%
Trump>Biden>Sanders: 22%

Okay, so lets say they all approve their top 2:

Biden: 77%
Sanders: 78%
Trump: 45%

Okay we have president Sanders! Congrats, right?

Well, now the trumpers who approved sanders are like: “Hey wait a minute, we made our daddy lose because we approved Sanders”

All the trumpers now have a meeting and decided that next election, they don’t approve Sanders or Biden as a strategic vote.

So now, Election 2 Results:

Biden: 55%
Sanders: 55%
Trump: 45%

Oh great, it’s a tie. The law says that the election have to be re-done to solve the tie:

Now this next election, all people who preferred Sanders first go to a Sanders supporter meeting and started saying: “Lets disapprove Biden so Bernie can win!”

Simultaneously, Biden voters will be like: “Lets disapprove Sanders so Biden can win!”

Next election results:

Trump: 45%
Biden: 30%
Sanders 25%

Congrats, we have a glorified FPTP and spoiler effect yet again!

Now, other election systems could also have strategic voting, but its less likely with, for example, RCV, since you can rank candidates.