Approval voting is very sensitive to strategic voting. Outside of toy elections where people are altruistically trying to find the best candidate, it reverts to similar dynamics as First-Past-the-Post.
bayesian regret and voter satisfaction efficiency calculations show approval voting generally outperforming alternatives such as instant runoff voting ("ranked choice voting") with any mixture of strategic or honest voters.
https://www.rangevoting.org/BayRegsFig https://rpubs.com/Jameson-Quinn/VSE5key
part of the reason this happens is that the IRV/RCV tabulation mechanism flat out ignores much of the preference information on the ballot. https://www.rangevoting.org/IrvIgnoreExample.html
approval voting is also just much more resistant to gamesmanship. it satisfies the "favorite betrayal criterion", meaning it can never hurt you to support your favorite candidate with approval voting. for instance, my aunt voted for biden even tho she preferred warren, to try to stop trump. if she had been ranking them in a single IRV/RCV election, she would have analogously ranked biden in 1st even tho she preferred warren. this kind of tactic means electability is still key, and it disadvantages third party and independent candidates.
with approval voting by contrast, she might strategically vote for biden (her 2nd choice) but she would still be free to also approve warren, as that could not possibly cause a worse outcome for her.
the center for election science has a good compilation of the best articles on tactical voting.
https://electionscience.org/library/tactical-voting-basics/
there's also an excellent book on the topic, called "gaming the vote".
https://www.amazon.com/Gaming-Vote-Elections-Arent-About/dp/...
If someone is favoured by a large enough group, they're supposed to win.
The point is what happens when people aren't fanatical but are forced to vote as if they were.
In a single winner election AV makes coordination among moderates somewhat easier, so it's an improvement, but still inferior to Ranked Choice/STV with multi-member districts.
I was mostly thinking about single-winner elections because the big headline elections in the US are all single-winner.
https://rpubs.com/Jameson-Quinn/VSE5key
Your scenario is unrealistic because real humans aren't that tightly clustered, so you get defectors. And people vote strategically. The winning position is the centroid.
https://www.rangevoting.org/AppCW
It is not known whether proportional representation can compete with the best single winner voting methods. We don't have enough data and we can't do multi-winter Bayesian regret calculations confidently. Here's an article you really should read if you think proportion representation is the answer.
A. The research compares proportional (PR) methods to plurality voting, the worst single-winner voting method there is. But superior methods like score voting and approval voting roughly double the accuracy (i.e. group welfare) compared to plurality voting. So no, there's no research showing the superiority of PR to these methods.
B. Even in that limited comparison, of PR to plurality voting, the data still is actually not that clear. For instance, Canada uses plurality voting rather than PR, and is rated as one of the most high functioning democracies by The Economist. Meanwhile lots of proportional democracies are far worse than plurality countries. Compare proportional Brazil (and several other Latin countries) to non-proportional UK, Canada, and USA.
I don't know the metric you are using here, but it is surely purely academic, as the rest of your comment. The idea that a single candidate can better represent a smaller (and usually gerrymandered) district than a larger number of diverse candidates in a larger district flies in the face of everything we know about real democracies and party systems.
> Your scenario is unrealistic because real humans aren't that tightly clustered, so you get defectors.
Again, theoretical claims against real world experience. I've experienced polarization in AV to the point where center becomes a wasted vote, and people are incentivized to support one of the two dominant slates.
Perhaps you were using one of these variants.
https://en.m.wikipedia.org/wiki/Multiwinner_approval_voting
You should probably specify to avoid confusion.
This is simply not correct. Elections are a form of statistical sampling, and with a good single-winner voting method, all voters of every stripe affect the centroid position, "tugging" it left, right, etc. Which you can see graphically depicted here.
https://www.youtube.com/watch?v=-4FXLQoLDBA
> Again, theoretical claims against real world experience.
You're not citing any real world data that contradicts my argument.
> I've experienced polarization in AV to the point where center becomes a wasted vote, and people are incentivized to support one of the two dominant slates.
If you mean "alternative vote" (known to experts like myself as "Instant Runoff Voting"), note that I'm not advocating that. I'm advocating cardinal methods such as score voting and approval voting. Which tend to elect broadly appealing centrists.