[EM] Vote transfer problems - plurality rule

[Kristofer Munsterhjelm]

On 2024-09-11 19:52, Abel Stan wrote:
> Hello everyone,
> 
> here I am with another musing on an uncommon type of mixed system, which 
> is basically the mixed (two tier) equivalent of STV with group voting 
> ticket only: Voters vote for individual candidates in their local 
> districts, and their votes get transferred to their party if it is not 
> "used up".

I'll have to look at this later, but I was just wondering if making a 
method that supports biproportional apportionment would solve the 
problems of MMP.

For simplicity (since the math is easier), consider a cardinal 
optimization method where parties and districts are given weights, and 
one vote (approval or full rating) is multiplied by the district weight 
times the party weight. Then perhaps we could run something like 
Pukelsheim's method with the upper apportionment being the result for 
the country as a whole.

If possible, such a method would allow voters to vote for candidates 
belonging to some party, but without having closed list, since the base 
method would be a candidate-centered method. It would just be one that 
weights votes to get the right upper apportionment.

The question is whether it could be done, though, or if the interaction 
effects would make it impossible (e.g. lowering one's rating of A turns 
the council from {A,X} to {B,Y}, which means that the number of X party 
seats changes based on the weight given to party A).

(I would prefer the method to be ordinal, but cardinal is easier to deal 
with mathematically; it's better to start on easy mode when trying to 
figure out if the thing is at all possible :-)

-km