[EM] Generalized Bucklin PR 2.3, basic PR examples

[Olli Salmi]

At 14:08 -0400 23.8.2003, John B. Hodges wrote:
>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 Phragmén's 
first method, which was proposed in Sweden a hundred years ago as an 
improvement to Andræ's method, except that Phragmén 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-Phragmén 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