Another combination to consider is Open List/Approval. Craig Layton, a (former?) member of this EM list proposed an Open List system in which each voter can approve as many members of as many lists as desired. The D'Hondt rule (based on total approval of candidates on the list) is used to decide how many members of each list will be elected. Multiwinner Approval within lists is used to decide on which members of the list will be used to fill the D'Hondt quota for that list.
As Bart pointed out, if there were only one candidate per list, the method would be multiwinner plurality (a crude PR method), and (on the other extreme) if there were only one list, the method would be ordinary (non-PR) multiwinner Approval. This suggests using PAV to select the list representatives instead of plain multiwinner Approval. There is another refinement that I have suggested. If voter V has approved only k candidates on list L, and approved a total of m candidates on other lists, then that voter's influence on which of list L's members should be used to fill that list's D'Hondt quota should be proportional to k/(k+m). In other words, voters that devote all of their votes to the success of list L should have more influence in deciding which members of list L fill its quota. Craig thought that this might decrease the incentive for voting across list boundaries. He's probably right on that. Perhaps a compromise based on the square root of (k/(k+m)) would be better. Craig also had the option of voting for the list as a whole, which would affect the D'Hondt quota for the list without helping to determine the representatives from the list. I believe that some variation of these ideas will prove to be as good or better than any List/STV combination, especially when simplicity of ballot is a consideration. Forest
