Vertical composition of multiwinner approval methods
I want to introduce a technique of combining two multiwinner approval methods using what I call vertical composition. The basic idea is that there are two "phases", both of which use approval ballots as their inputs, and the first phase filters out some candidates from entering the second phase. Voters, however, do not cast simple approval ballots, but ballots with trivalent values for each candidate - it is important to note that this is distinct from 0-1-2 score voting. The values are as follows:
- Approve in both phases (AA)
- Approve in first phase, disapprove in second phase (AD)
- Disapprove in both phases (DD)
The hypothetical fourth value, Disapprove in the first phase and Approve in the second phase, is excluded because it doesn't make sense.
My basic use-case for this technique is when the first phase is simple bloc approval voting that filters out anyone with more than, say, 75% disapproval (this threshold is a parameter), and the second phase is some proportional approval voting method.
This specific method would be useful for an organization that wants proportionality in its internal democracy but also wants to set up a barrier to prevent bad actors ("entryists") from joining the organization and winning a few seats proportionally while antagonizing everybody else in the organization. Voters would use DD votes to filter out the bad actors, and AD votes for candidates from different factions that are participating in good faith. A relatively high first-phase disapproval threshold, such as 75%, would make the method resistant to people overusing DD votes.
@isocratia does there need to be more than one phase? Why not have a single phase and remove candidates without sufficient support before a restricted proportional approval?
@cfrank That's what I said, the "phases" are part of the algorithm and voters only cast a ballot once.
@isocratia yes I understand the definition of the method you described. But what I mean is, what does the second phase and the two-phase-approval ballot introduce that could not be encoded with just the one phase and an ordinary approval ballot?
@cfrank The first phase would eliminate some candidates who might otherwise win in the second phase.
These would be candidates who've actively antagonized everybody outside their faction. In order for the first phase to matter, such a faction would have to be smaller than 1 - the first phase disapproval threshold, but large enough to win at least 1 seat proportionally.
Believe it or not, I was in an organization that was faced with such a scenario. They were using STV and the troll faction's candidate came in 1st because they all bullet-voted for him.
@isocratia yes it is sufficient to serve that function, my question is about whether the second phase is necessary to induce the same functionality. It seems like one could impose an approval threshold to remove undesirable candidates, and then proceed from there with a proportional approval method over the remaining candidates, requiring only a single approval indication. Is there something wrong with this?
That could end up removing candidates that many voters regarded as unrepresentative of themselves but not antagonistic to them.
The idea is that voters would use AD votes for factions that are potential coalition partners for their faction. Some voters can be expected to overuse DD votes, which is why the first-phase disapproval threshold is high.
@isocratia hmmm I still would like to see an example of the difference. Like I said I think your method is sufficient but I’m not sold yet on the necessary part. It might not matter anyway since sufficiency is by definition good enough! But I’m just curious.