Arrow's Impossibility Theorem | Hacker News Reader

Arrow's Impossibility Theorem

en.wikipedia.org

14 pointsweatherlight7 comments

non-mathy explainer why ranked choice voting isn't great.

https://www.youtube.com/watch?v=Q60ZXoXP6Hg&list=PLlwsleWT76...

This should be required reading for all Australians

Australians have an insufferable lack of understanding of why their voting system, which they think is perfect (or at least significantly better than any other)

simply isn't

Arrow's impossibility theorem has 0 consequences in the real world. It's nothing but fancy math that some professor thought up to impress his professor pals.

Split votes are definitely a real phenomenon that have occurred in many real world elections.

Perhaps, but AIT doesn't actually give any useful information about the phenomenon of split votes. It doesn't tell you how likely they are, or give any statistical insight into the effect at all.

Anytime there is an election, it is always technically possible that people's preferences are uniformally distributed and no electoral system could ever give a good result. That's basically all that AIT says.

Arrow says you can only have 3 of the 4 properties in the theorem, but it doesn't say anything about other properties, and it doesn't say which of the 4 properties is most important. And if you bend the rules, it doesn't apply (e.g. random dictatorship).

This is kind of like saying one database isn't better than another because CAP theorem exists. Sometimes you prefer one of C or A, or a bad database is missing both C and A, or one has better licensing.

That's kind of the point though? When they say their voting system is perfect or the best, they're just saying it because they've been told to think so, not because they have a meaningful understanding of which properties their system satisfies, and why those are better or more important than those satisfied by other systems. There's 0 understanding of the tradeoffs.

By all means, if someone does know about all this and makes a well reasoned case that their preference is for this system and why, that's one thing, but that's not the case with 99% of the Australian voting public.

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