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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.



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