[EM] Resume: Proportional multi-winner ranked voting methods - guidelines?

[Kristofer Munsterhjelm]

On 06/04/2017 07:26 PM, VoteFair wrote:
>> ...
>> The LCR example is a concrete example that giving the
>> first seat to the CW makes the method fail Droop
>> proportionality.
>
> I do not regard Droop proportionality as an important criteria to meet.
> It is based on looking at each ballot one candidate at a time, right?

Not necessarily. It's a multiwinner generalization of mutual majority.

Mutual majority says: If there's a set of candidates that a majority 
ranks ahead of everybody else (but not necessarily in the same order), 
then someone from that set should win.

Droop proportionality says: If there's a set of k candidates, and at 
least p Droop quotas worth rank all of these ahead of everybody else 
(but not necessarily in the same order), then min(k, p) of those should win.

STV passes Droop proportionality just like IRV passes mutual majority. 
But Droop proportionality doesn't imply STV (as in the IRV-like method) 
more than mutual majority implies IRV. Most Condorcet methods also pass 
mutual majority, as electing from the Smith set implies the criterion.

There may be a bit of confusion because methods that pass Droop 
proportionality are sometimes called STV methods, e.g. as in Schulze STV.

Perhaps Droop proportionality isn't the exact proportionality measure 
one would want - for instance, for my Bucklin methods, I've tried to 
base them on divisor methods rather than on hard quotas - but I think 
the concept that "some voters who broadly agree on a group of candidates 
should see one of them elected" is a good one. That is, that a group of 
voters can have "their" seat without having to agree on a strategy.