No, I'm not putting this in /c/electoralism , for reasons found in the third paragraph
Most people know there's first-past-the-post and there's ranked-choice. But I've recently learned there's a much longer list than that, and they all have pros and cons.
Somecomrades would say 🙄yeah bourgeois elections who cares🙄 but that is wrong: the mathematics applies to all voting. It's the engineering side of the question: "If we have a bunch of people, maybe a hundred, maybe a million, how do we decide what the collective will is in the fairest way?" The name of the field is social choice theory because a social group is trying to make a choice.
You: oh bourgeois elections are a farce lol
Me: exactly and that's why we need to study how can voting be not a farce
First-past-the-post gets a hard time, and deservedly so. But the people who say "first-past-the-post bad, ranked choice good" are oversimplifying. It turns out there are all these mathematical trade-offs, and it is formally provable that there is no perfect system.
Most ranked choice voting systems* can suffer from a crazy effect where getting more votes makes you lose. The technical name for this is a monotonicity failure because mathematicians are shit with names. (*There are theoretical ranked-choice votings that don't fail monotonicity, but I don't know of any being applied in a political system. Companies probably have used them.)
In the 'Popular Bottom' Scenario, 
gets 45% of the vote and isn't elected; but in the other scenario he gets 39% and is elected. What happened is he lost supporters to a rival (Top) who eliminated his other rival (Center) for him, so he was able to sneak in.
First-past-the-post doesn't have this problem: more votes is always better. But it has plenty of other problems. The USA system fails the no favorite betrayal criterion catastrophically; that's the criterion that you should be able to vote for who you like best. Usans "have to" vote for a candidate they hate.
This page summarises it pretty well: https://en.wikipedia.org/wiki/Comparison_of_voting_rules with tables comparing the different traps multi-winner systems fall into and the traps single-winner systems fall into.
Some cool systems:
-
PDF – "This paper discusses the protocol used for electing the Doge of Venice between 1268 and the end of the Republic in 1797"
Anyway, interesting stuff to think about if we design democratic/anarchistic systems for collective decision-making. It wouldn't have to be electing representatives, it could be voting on policies, same maths either way.
I agree that figuring out ideal voting systems is an exciting endeavor, and different systems can be more or less appropriate. However, I completely fail to see how the Wikipedia examples represent a "failure" of ranked choice voting.
For the first election: you're making it sound like Bottom receiving the plurality of votes (45%) in the first round is causing it to ultimately lose. This is not true, Bottom loses because the majority of voters (55%) prefer Center to Bottom which is made clear in the second round after elimination and transfer of preferences from Top. This is good, this is the point of RCV and why it is vastly superior to FPTP.
Now for the second election: claiming that Bottom is all the sudden unpopular and therefore them winning is a bad thing is doing a lot of heavy lifting here to try to make ranked choice voting look bad. Why did all 6% lost from Bottom go into Top but then Center is split exactly down the middle in terms of preference? Those circumstances seem artificially contrived to me and not very reflective of how overlapping ideologies between parties would actually interact, especially as in the previous election the entirety of Top goes to Center as their 2nd preference (not calling you out but the sus wikipedia example). Again, the result is that
The reason I'm going kind of hard here, and I might be going a little crazy, is because I really feel like all this sudden RCV hate is very suspicious. I've had several otherwise "woke" and more-progressive-than-not friends sharing TedX videos giving similarly contrived situations to show that RCV is actually really bad and can totally be just as undemocratic as FPTP (their example was literally about where to put a refueling base for 4 weirdly spaced out Mars colonies). Then there was the recent Veritasium video about how voting is imperfect and can never be solved!!1! (So why bother, right guys?) And yeah, I get this weird feeling that even this incredibly simple reform that could bring a trifling of more authentic democratic representation to our Bourgeois Dictatorship of Capital that we call American Democracy is somehow getting psyoped against in order to maintain the two-party dictatorship. Like, all the big pop science entrenched youtube channels creating these kinds of videos just seems like a PR campaign to specifically dissuade those bazinga types that at least should be able to understand on a logical/mathematical level that RCV is much better.
Anyways, my main take is RCV is good and quite literally always better than FPTP. It's the simplest reform that should be default on any liberal party's platform if they weren't deeply unserious. Whether we end up even having direct elections of representatives or multi-option direct ballot initiatives in socialism I don't feel as strongly about, I'm open to all kinds of ideas. But don't let the RCV hate spread uncritically. If I'm totally off base than someone explain below cause I do feel like I'm going a little crazy here.
Yeah, because you have to come up these weird little tortured examples to make the system that determines outcomes based on the couple percent of the population that live in particular states seem okay
Empirical and theoretical studies are both needed.