Aaron Armitage wrote:
I've considered the question myself, although I've never described my
ideas publicly. Now's as good an opportunity as any.

[snip]

The first way of adding lists to STV is simple: you list your candidates,
and last you put a list, which fills out the rest of your preferences
according to the predefined order of the list. I suppose you could include
more than one list, or a list then a candidate, but that would be
pointless because your vote would be used up.

A simple example: The Yellow list is A>B>C>D>E, and
the Brown list is F>G>H>I>J. If you vote B>I>Yellow, it counts as
B>I>A>C>D.

An advantage of this is that you can vote "cross-list". I think the ballot design would be challenging, though; in order for the voter to be able to vote cross-list, the preference ballot would have to reference all the candidates on all the lists, so that the voter can vote B ( which is on the Yellow list) > I (which is on the Brown) > lists.

The second way is more sophisticated, and much more complex to count. The
vote itself needn't be any more complex (you could always just vote a list
and leave it at that), but it can be, and depending the layout of the
ballot it may look more visually confusing. It will really need to be done
with a touch-screen, preferably using a drag-and-drop interface. A paper
ballot should be printed out and kept as a check (or perhaps the paper
count should be all there is, the computer interface being simply the
means of generating the paper ballots).

Instead of using regular STV, the second way uses CPO-STV. Since it's a
Condorcet method, it allows tie votes which amount to voting present in
the choice between them. Or, in the case of CPO-STV, between two outcomes
which differ only in electing one or another of tied candidates. The lists
are unordered and instead of representing a completed ordering filled in
at the end of the ranking, they are a tie between all list members. The
party lists will probably be mutually exclusive, but there's no reason not
to have other lists which overlap the party lists and each other. If a
candidate appears in two lists which are ranked on the same ballot, he
takes the higher of the two positions, but if he is ranked individually,
as a candidate, he takes that rank regardless of how any of his lists
might be ranked.

So, going back to the previous example, say you vote
B>Vowels>Yellow>Brown>Purple>F>White. This becomes:

B > (A,E,I,O,U,Y) > (C,D) > (G,H,J) > (K,L,M,N) > F > (P,Q,R,S,T)

You could also use Schulze STV -- if the lack of polynomial runtime isn't a problem. For lists, you'd have many candidates, so it might.

For the sake of completion, I can also mention that in my monotone Webster-based multiwinner method, the "rank within a list" and "expand list to preference ballot" methods would have the same outcome. This is because the method has the property that if everybody votes preferences in a disjoint manner - i.e. no cross-list voting - then each party is given a number of seats equal to how many they would have got if voters voted for the party list and the seats were apportioned by Webster's method. Thus that method would be the closest to bridging lists and preference ballots, because voting in a "list fashion" gives the same result as actual party list voting. Unfortunately, that method is not polytime either, and the single-winner results are not very good. It's more a proof of concept than anything -- maybe it's possible to retain that "list similarity" property in better multiwinner methods.
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