That all said, full ranking systems are definitely the superior option, and I’d certainly take approval over our current state.
No. Approval voting has been extensively studied by game theory experts like NYU political science professor Steven Brams, and found to be one of the most resistant to tactical voting. Computer simulations show it performing exceptionally well even with highly strategic voters.
https://www.rangevoting.org/BayRegsFig.html
https://rpubs.com/Jameson-Quinn/vse7
There's even a mathematical theorem (proof) that, given plausible strategic behavior by voters, approval voting always elects a beats-all "Condorcet winner" when one exists. This is mild (some would say GOOD) reaction to strategy.
https://www.rangevoting.org/AppCW
> Checking approve on someone I believe to be more popular than my favorite candidate lowers the chance my favorite candidate wins.
Yes, this is beneficial not harmful. The alternative is that the voting method must ignore all preference data about the relative support of X vs. Y as long as the voter prefers X to Y. That causes big problems.
https://medium.com/@ClayShentrup/later-no-harm-72c44e145510
It is precisely why ranked voting methods like Instant Runoff Voting are so vulnerable to tactics. If I prefer the Green, my general best strategy is to tactically rank the Democrat in 1st place, thus "burying" the Green and making the mere appearance of un-electability a self-fulfilling prophecy.
https://www.youtube.com/watch?v=JtKAScORevQ
https://www.rangevoting.org/NESD
The major moral of voting theory is to AVOID RANKED VOTING METHODS, favoring RATED voting methods like score voting, STAR voting, and approval voting. Here's a presentation I gave in 2015 to the Colorado League of Women Voters explaining more.
https://www.youtube.com/watch?v=HyBm_Hcu4DI&t=488
I would also recommend the 2008 book "Gaming the Vote". Full disclosure: I'm in it.
scorevoting.net/IrvIgnoreExample.html
I would disagree about Condorcet. Score voting and variants, such as STAR voting and approval voting, are vastly simpler than any ranked method, and perform better in voter satisfaction efficiency calculations, and plausibly make better Condorcet methods than real Condorcet methods.
https://www.rangevoting.org/AppCW
The biggest moral of social choice theory is: avoid ranked voting methods.
The problem is that IRV/RCV doesn't capture your preferences, because it ignores all your preferences except your top choice, until your top choice is eliminated. IRV is reasonably good at making sure that third-parties can't prevent first-parties from being elected, but very bad at actually allowing third parties to actually be elected even if they have widespread approval.
Approval is a good compromise, and fully ranked systems (e.g. Condorcet) would be even better but much harder to enact. I would happily support universal adoption of Approval.