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I think you may be confusing IRV and STV. STV is the multi-winner version of IRV, intended to produce proportional representation.
As for defending IRV:
Clone independence is a huge deal. It is a much-bigger deal than what sort of candidates get elected, because it gives an escape valve against leaders going corrupt (since a clone can steal their seat). Approval voting is also clone-independent, but there are a ton of voting systems that aren't.
Approval voting has a massive tactical voting problem. Specifically, an approval cutoff (that is, when you rank the candidates in order of preference, the point at which you stop approving) that does not divide the viable candidates wastes your vote. This is in play most of the time for most voters. Rampant tactical voting cases are bad because they disenfranchise the honest and principled in favour of the unscrupulous, and the world has more than enough of that. Its tactical voting problem is not as bad as plurality, but it is close. Now, of course, there is no system that never has tactical voting except for random-ballot (i.e., pick a ballot paper at random, and whoever's on that ballot wins), but IRV does much better than most in this regard; in most cases voting your true preferences is correct.
IRV does not directly advantage compromise candidates. However, it's one of a few systems that if paired with compulsory voting invoke the Median Voter Theorem, and that does tend to produce compromise candidates. I'm not sure that approval does; I think maybe it might if everyone were to vote his/her true preferences, but that's not going to happen because of #2.
STV run with one seat and a 50% quota (under most methods of doing STV) is equivalent to IRV. I prefer the mental abstraction of STV, but your right that it isn't common parlance to use it in that way.
IRV is clone independent but still falls to the center squeeze (where several nearby candidates can choke out the center of the group). Also, every single Condorcet method is clone independent if there exists a Condorcet winner (which polling suggests is over 90% of elections). Many of these algorithms will choose something from the Smith set where it isn't even clear mathematically what you could do that is better, it just chooses a different one from the Smith set if there are clones. These are all ranked choice systems that can be computed in a single pass over the ballots. Why are we looking at IRV among the ranked choice methods?
Approval at least has the guarantee that you should never rate something you like less higher than something you like more. Approval and IRV have relevant tactical voting in the same situations: when your preference is close to losing to something more moderate. Both ask you to downrate the moderate if you think you can win, or uprate the moderate if you think you can't. IRV requires you to tell an outride falsehood to do this. In terms of the benefit you get from tactical voting, it is pretty similar across the two methods (both about 10-20% of what you get in FPTP).
IRV does not choose a Condorcet winner, and thus does not invoke the Black median voter theorem. There are many ranked choice algorithms that do, but not IRV.
Yes. There's a solid argument for some of the better Condorcet-completion methods as better than IRV, despite them failing later-no-harm. Approval is not a Condorcet method.
I... suspect you're not counting things as tactical that are, in fact, tactical. Honest voting in approval is approving everyone better than some fixed standard of goodness. This usually doesn't split the viable candidates (i.e. you approve all of them or disapprove all of them), which means your vote is fully wasted (just as with voting third-party in plurality). To make your vote count, it usually has to be tactical - to take note of which candidates are viable and choose a cutoff that splits them.
IRV has tactical voting a little bit of the time for some voters. Approval has tactical voting literally all of the time for most voters.
I only bring up Condorcet as if we are going to be doing ranked choice ballots we have all these other better options. Options where counts can be aggregated from different polling centers and that provide better mathematical guarantees. I don't think later-no-harm is a good outcome. If a candidate B becomes more popular with a subgroup, but doesn't reach the threshold of being their first choice, candidate B should be more likely to win the election. I'd much rather have monotonicity, so that rating a candidate higher makes them more likely to win.
I'll grant that your threshold choice is inherently tactical, but I think it is a much better brand of tactical than other things that fall under the label. In IRV, tactical votes are misrepresenting your preferences to the voting system. You have to lie about who you actually like and dislike. In approval voting, you are compressing down the vote to provide as much information as possible to the voting system. It is a "true preference" that you like everyone you voted for more than everyone you didn't. It doesn't reward liars, it rewards those in touch enough to know roughly the bounds of possibility for this election.
But yeah, I guess there are some real selling points of IRV:
-a lot of the other ranked choice methods aren't clone independent which is definitely a problem that needs a solution
-you can just walk in and list your candidates in order and be voting "optimally for your desired outcomes" a good chunk of the time.
I still think ranked methods aren't worth the cost (really try it, with a group of even 5 people trying to decide what to do, ranked methods are demolished by approval voting in terms of implement-ability, then extend to the entire country). IRV among them is particularly bad for counting but is among the better set of election properties and especially explain-ability.
(Also, you've been a great conversation partner, kudos and gratitude)
Inherently, no, but later-harm produces tactical voting. Worse, it produces tactical voting in a mass-producible way; political parties will figure out which full ballot by their supporters will be best for them, and push it hard. Full how-to-vote cards are a thing in Australia, but the parties don't push them all that hard due to later-no-harm.
Now, yes, later-no-harm is incompatible with a bunch of other criteria, which is annoying. But, well, impossibility theorem.
I mean, yes, the O(N!) worst-case is a pain. I will say that it's not nearly as bad in practice as the worst-case; a good number of seats in Australia have [#2 > all votes other than for #1 and #2], which simplifies it to 2 buckets (and a lot of the rest have [#3 > all votes other than #1/#2/#3], which simplifies it to 6 buckets). Usually the AEC can predict this ahead of time; they do a full recount if their prediction is wrong, of course, but most seats are known within hours.
(STV absolutely always is a nightmare, though; we use it for our Senate, and it takes over a week to count. AIUI it's worse in terms of tactical voting, too.)
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