SO: In this example, GB 2.3 seems to perform OK as a method of PR. I invite suggestions for harder cases.
It should work all right as a PR method, if I understood it correctly. GB gradually changes preferential ballots into non-preferential, or approval ballots if you prefer, so it should in principle work very much like STV. If all ballots were non-preferential, the method would be like the so called Phragm�n's first method, which was proposed in Sweden a hundred years ago as an improvement to Andr�'s method, except that Phragm�n used the Hare quota. I see no reason why a mixture of a preferential and a non-preferential method shouldn't work.
I think it would also be possible to count the next preferences only in the ballots that belong to the lowest candidate, instead of all the candidates. So instead of elimination you count the next preferences. The ballot is still transferable but you let the other voters decide the order, within limits. I don't know how this principle would work with IRV.
You could also reduce the value of votes according to the d'Hondt-Phragm�n method.
As for Bucklin, Norway uses a Bucklin-like method for ordering candidates on the party list. The first candidate is the one with the most first preferences, the second candidate is the one with the most first and second preferences, and so on. I remember reading that this method was used in Finland when the professors of the University of Helsinki nominated three candidates from which the chancellor was appointed. The system of proposing three candidates for appointment was used in Sweden in the 18th century, so this method may have its roots there.
Olli Salmi ---- Election-methods mailing list - see http://electorama.com/em for list info
