For elections to President of Ireland, there is only one 'seat' available. And it is elected under PR-STV. The PR-STV system works fine with only one seat. You select the quota the same way, you do transfers the same way. Ireland uses PR-STV for single-member constituancies just fine.
This is, at the end of the day, mostly semantics but you can't have proportional representation, in a vote that only elects one person. It's not possible for someone to be 40% blue party and 60% red party, because there's only one of them. So, in Ireland votes for the president, and for by-elections to replace a single member use AV.
STV and AV (and a bunch of variants of each) are closely related, but they do have differences, and repeatedly claiming that one is the other, when they're not, isn't that helpful to the conversation.
> This is, at the end of the day, mostly semantics but you can't have proportional representation, in a vote that only elects one person.
Proportional representation is really a matter of degree rather than a binary categorization -- a system doesn't magically become proportional when you apply it to a two-member constituency that would be not-proportional when applied to a single-member constituency.
OTOH, the maximum degree of proportionality you can achieve in an electoral system increases with the number of seats that are elected by the same set of ballots.
STV is an election method defined for any arbitrary number of seats, IRV/AV is exactly STV applied to a single-seat election.
This is not correct. PR-STV requires multi-member constituencies (as they have in Ireland). AV is single-member constituencies and isn't PR.