Accent

There are phrases that Jorie pronounces with a distinctly Australian accent just from watching the Wiggles.

Arrow's Theorem, voting systems, and the folk power of impossibility theorems

Addendum #2: I apparently completely mischaracterized Patrick's actual position here; I thought he was impugning Arrow for even proving the theorem, whereas it appears his concerns are more about its misuse. I both apologize to Patrick and would request that people cool it a little in the comments.

nhw makes a provocatively titled post called "Why Arrow's Theorem is wrong", and pnh links to it on Making Light with title text implying that mere interest in it has dark motivations: "Oddly enough, there's always a ready audience for intellectuals willing to argue that democracy is impossible".

Sorry, but I have to call shenanigans on this--to some degree.

First: nhw is saying that the theorem's stated desiderata are not really necessary for a good voting system. A theorem isn't wrong if its assumptions are inapplicable; its assumptions are just inapplicable. The reason I want to be pedantic here is that I'm pretty sure there's an extensive crank literature attempting to prove Arrow's Theorem literally incorrect, just as there's an extensive crank literature on squaring the circle or disproving Fermat's Last Theorem. I've seen people propose all manner of voting systems that they claim violate Arrow's theorem through some loophole or other and therefore prove it wrong; of course, they're just systems that violate one or other of the proposed requirements in a way that's considered harmless or irrelevant.

Second: While it's possible to argue that universality, independence of irrelevant alternatives, and monotonicity are not really necessary, it's nevertheless true that people have complained about these things as problems in real-world voting systems, and I think it's therefore still an interesting result that you can't have them all in a reasonable system, whether or not one is an evil antidemocrat. It's not universally true that failure to organize a winning coalition is blamed on the losers. People constantly grouse about the prevalence of "spoiler effects" in American elections, which is the "independence of irrelevant alternatives" condition. It's usually claimed that egregious failure to satisfy independence of irrelevant alternatives in presidential elections is the reason why the US is locked into a two-party system, which is held to be very bad by advocates of third parties. It's common for libertarians and left progressives to claim that this is the main impediment to constructive change in the American political system. There's more to it than that, I think, but it's certainly part of the story.

That said, it's true that, as I've said before, impossibility theorems like this can have a sort of folk-theorem power that exceeds their real applicability, and this is a real danger. My understanding is that Arrow's theorem relies heavily on things that rarely happen in, say, American elections, such as the existence of "Condorcet cycles" in which a majority sincerely prefers candidate A to candidate B, a majority prefers B to C, but a majority also prefers C to A. If you accept that you're not going to handle Condorcet cycles gracefully, you can do really well with everything else--a lot better, in fact, than the systems typically in use in the US generally do. So nhw has a point--I'm mostly arguing with the post title here. The true lesson is that when you're confronted with an impossibility theorem saying that something universally desired cannot be had, you should always read the fine print.

But Arrow's Theorem is also applicable to things other than democratic government. samantha2074 is a big fan of figure skating, and I know there's been a lot of dissent and upheaval in recent years concerning scoring systems. The prevalence of "flip-flops" causes a lot of grief: situations in which contestant C scores in such a manner as to reverse the relative rankings of contestants A and B. Usually, people blame the system for this. Phenomena such as Condorcet cycles are pretty common in figure skating, much more common than in political elections, and I don't think it's evil or antidemocratic to note that you're always going to have to settle for a system that sometimes has some sort of paradoxical result.

Addendum: Sam reminds me that "flip-flops" were a feature of the pre-Code of Points ordinal-based system, and are not present in the CoP. However, I do recall that the flip-flip phenomenon was widely discussed during the debate over changing the system.