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Comment by DougBTX | Hacker News Reader

> Where's the paradox?

Exactly. I propose that the paradox is in first-past-the-post voting, a 5% swing leads to a 100% change in representation. How can that be?

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Relax - they're all broken: https://www.investopedia.com/terms/a/arrows-impossibility-th...

Arrow’s impossibility theorem only applies to ranked choice voting systems.

Yes, but what I mean is that even if you move away from FPTP voting, the others all have compromises.

But for many the drawbacks of ranked choice systems are far more preferable to those of FPTP. Additionally, Arrow's theorem only states that the spoiler effect cannot be completely eliminated by ranked choice - it says nothing about how often such an event actually occurs, and in practice spoiler candidates will occur less frequently with ranked choice systems compared to FPTP.

Additionally, rated choice voting systems are not subject to Arrow's theorem.

... which are almost never used in voting for governments.

FPTP is a ranked choice system.

No it isn't.

https://en.m.wikipedia.org/wiki/Ranked_voting

> The most commonly-used example of a ranked-choice system is the familiar plurality voting rule, which gives one "point" (vote) to the candidate ranked first, and zero points to all others (making additional marks unnecessary).

This is not what is usually meant with the term (plurality voting is different from ranked voting where there are non-trivial preference orderings) and in any case not what the Arrow theorem applies to.

Arrow’s theorem defines a ranked voting system as a function that takes a permutation of the candidates for each voter and outputs a single permutation of the candidates. As a special case, if you take the function which sorts the candidates by how many voters ranked them as first, you get plurality voting.

And that makes plurality voting different from ranked voting where the voters can submit arbitrary preference orderings. In any case, as I said, the Arrow theorem doesn't apply to plurality voting, as there can be no cycles in the aggregate.

Only if you reject the axiom of choice: https://www.jyotirmoy.net/posts/2013-10-28-arrow-ultrafilter...

Only if you have infinite voters.

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