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

[Kristofer Munsterhjelm]

On 06/06/2017 12:43 PM, Toby Pereira wrote:
> Just to finish the thought on this, under Sainte-Laguë/Hare
> proportionality , for a party/faction to guarantee themselves s seats,
> then I think they would need s-1 Hare quotas and then a Droop quota
> for their last seat, but it would be a Droop quota considering only the
> remaining seats and voters rather than all of them.

Every divisor method will sometimes fail quota 
(http://www.rangevoting.org/Apportion.html). Conversely, no static quote 
will do if we want the method to reduce to a divisor method. So 
something more sneaky will have to be done if a candidate-based 
multiwinner method is to be "divisor method-like" rather than "quota-like".

On a related note, I'm kind of curious if Hare and ordinary Sainte-Lague 
is too favoring of small parties. Hong Kong used/uses(?) Hare and, to 
quote Wikipedia, "in Hong Kong the use of the Hare quota has prompted 
political parties to nominate their candidates on separate tickets, as 
under this system this may increase the number of seats they obtain". 
But if it is, a slight adjustment is enough: countries using the 
modified Sainte-Laguë method don't seem to experience this splintering. 
Perhaps there are other reasons, e.g. ordinary Sainte-Laguë is fair if 
there's a per-party threshold that keeps single-candidate parties from 
being advantageous.