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Comment by alienjr | Hacker News Reader

https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...

Arrow's is widely misinterpreted. All it says is that you can't have a voting system that fits those four chosen criteria. It doesn't prove that those four criteria are required or even desirable. Independence of Irrelevant Alternatives is particularly problematic.

Also, with trade-offs there's always an efficiency frontier. You want to be at least on that frontier, and not worse.

Honestly, this likely presents the constraints too tightly. Dictators are likely ok (in the jargon of this proof)

Also, the theorem only applies to ranked-choice voting methods for single offices, so the kind of ordinary proportional representation list-voting used in parliamentary systems faces other constraints rather than those of Arrow's Theorem.

I interpret Arrow's theorem as a statement that there is no universally-agreeable definition of "fair". You can create local definitions of "fair", you can get people to agree to operate with them, but somebody else can always propose a different, sensible definition of "fair", and that definition may produce a different outcome. It also means that it's reasonable to debate the effects of different definition of "fair".

I'd say the entire point is precisely that these constraints, quite surprisingly, are too tight. You must loosen them. You have no choice.

It doesn't mean it's the end of all hope, it just means that it may not be quite as easy to "turn a crank" and get universal answers as we'd like.

I think a lot of people miss that Arrow's theorem is less a political statement than a mathematical proof, and end up bringing a lot of baggage to it that is not justified. It is what it is; it isn't morally "right" or "wrong", it isn't that it "misses something" or unfairly focuses on something else, it's just "true". What you do with it is up to you, but you won't change its truth or falseness value by arguing with it any more than you can any other proof.

There are a few odd mathematical theorems which almost just seem to draw cranks like moths to a flame: I don't think I've ever seen a reference to Godel's incompleteness theorem outside of a mathematics textbook which isn't eye-rollingly cringeworthy. Similarly with this one; we have very technical theorems that take years of study to fully understand, and they almost touch on other fields or have some kind of "wow factor" which makes them irresistible to pop lit writers like Gladwell, Hofstadter, etc.

It's not dictators that are ok, it's the overly strictly defined "independence of irrelevant alternatives"

It is entirely possible that reasonable voters will end up with a rock-paper-scissors situation among their top three preferences. Such a situation will "break" Arrow's theorem (rock wins an election vs scissors, but when paper enters now scissors wins).

But such a possibility doesn't mean your voting system is bad, it's completely fine to have that happen so long as one of the top rock-paper-scissors cycle wins. This property is true of a whole lot of voting systems that Arrow needlessly dismisses.

I'd also argue that if IIA exists, then it might be a good thing. For instance, if a voting population appears to have a clear preference, but then produces a cycle when a new candidate is introduced, it might just be an indication that the first set of candidates were lousy, the voters felt they were compromising, and the first set of candidates didn't represent voter preferences well enough.

Voters are always going to have to compromise. People are extremely complicated and different from one another. Even people who have been married for 50 years have a hard time agreeing on everything. Expand that out into millions of people and the scope for common ground narrows dramatically.

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