[EM] PR/STV Hybrid for multi-winner?

[Forest Simmons]

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