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

[Juho Laatu]

> On 04 Jun 2017, at 11:18, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
> On 06/04/2017 10:07 AM, Juho Laatu wrote:
>>> On 04 Jun 2017, at 07:55, VoteFair <electionmethods at votefair.org>
>>> wrote:
>>> 
>>> Yes, "proportional multi-winner Condorcet" has no clear,
>>> unambiguous meaning beyond the criteria for identifying the winner
>>> of the first seat.
>> 
>> Yes, it is not easy to say which methods should fall in the
>> "proportional multi-winner Condorcet" category. I also note that even
>> if it would be a requirement that the first seat shall go to the
>> Condorcet winner, if one exists, it is quite possible that the
>> Condorcet winner would not be elected if there are two seats. (e.g.
>> when there are two big parties, left and right, and one small
>> centrist party with a Condorcet winner)
> 
> The LCR example is a concrete example that giving the first seat to the CW makes the method fail Droop proportionality. E.g.
> 
> 43: L>C>R
> 41: R>C>L
> 6: C>L>R
> 
> number of voters = 90, Droop quota for two seats = 30, so both L and R should be elected, but C is the CW.
> 
> For larger assemblies, it might still be a good idea to give a few of the seats to winners chosen by a multiwinner method with few seats, or a single-winner method. Doing so would make centrists the kingmakers in a kingmaker scenario, rather than minor parties on one wing.

I guess we need to decide if we want to violate proportionality or seat monotonicity (if we respect the "first seat to the Condorcet winner" principle). Since the name of the category ("proportional multi-winner Condorcet") includes word "proportional", maybe in this case it is a smaller problem to violate seat monotonicity.

The problems may continue (with smaller probability) in larger assemblies. When the number of seats grows, in LCR examples (with a very small C party) we might elect first {C1}, then {L1, R1}, {L1, C1, R1}, {L1, L2, R1, R2}, {L1, L2, C1, R1, R2}, and eventually {L1, ... , L49, C1, R1, ... , L49}. If L and R have exactly the same number of votes, we may need to elect C1 when the number of seats is odd, no matter how small C party is. C1 will be a kingmaker if we have an odd number of seats, i.e. quite randomly.

Juho