With a single transferable vote, how are the transfers selected?

Question

With a single transferable vote, when a candidate's votes exceed the quota, the remaining votes are transferred to the next ranking candidate on each of the excess ballots.

However, how is it decided which ballots are selected to transfer? e.g. if the quota is 4000 and they received 5000 votes, then how are the additional 1000 picked?

I was told they were just picked at random but I've been reading a bit more from people supposing that maybe they calculate the proportions of the next ranked candidate and pick ballots that represent that proportion, or transfer all the votes but each is only worth a fraction of a vote depending on the excess and the quota. This seems very laborious and error prone, also I live in Ireland where we use STV and I've never heard of this being done.

Answer 1

Here is the wikipedia article on STV vote transfers in general, and here is a webpage describing the method for Ireland in particular. I don't want to post a link-only answer, but the description for Ireland is rather long, and that's just one method. In short, yes, Ireland transfers a fraction of the votes proportionally.

If a country were try to do it by hand, it would indeed be laborious and present numerous opportunities for error. The Wikipedia article mentions that one of the first methods was developed in 1969 with computers in mind. At that point, the computing power needed to implement the method was probably significant, but at this point a laptop could easily handle it.