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

Tue Jun 6 03:43:22 PDT 2017

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.
For example, let's say there are five seats.
To guarantee one seat, a party would need 0 Hare quotas and one Droop, so 1/6 of the total vote.
To guarantee two seats, a party would need 1 Hare quota and one Droop quota of four seats, so 1/5 + 4/5*1/5 = 9/25 or 0.36 of the vote
To guarantee three seats, they would need 2 Hare quotas and one Droop quota of three seats, so 2/5 + 3/5*1/4 = 11/20 or 0.55 of the vote.
To guarantee four seats, they'd need 3 Hare quotas and one Droop of two seats, so 3/5 + 2/5*1/3 = 11/15 or 0.73 of the vote.
To guarantee five seats, they'd need 4 Hare quotas and one Droop of one seats, so 4/5 + 1/5*1/2 = 9/10 = 0.9 of the vote.
I think this is correct now. According to the Wikipedia https://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions the Hare version of proportionality for solid coalitions requires a full Hare quota for each seat, but I think this is a more sophisticated definition.

      From: Toby Pereira <tdp201b at yahoo.co.uk>
 To: Kristofer Munsterhjelm <km_elmet at t-online.de>; VoteFair <electionmethods at votefair.org>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com> 
 Sent: Monday, 5 June 2017, 18:23
 Subject: Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?

I think that's wrong actually. Forget that last post!

      From: Toby Pereira <tdp201b at yahoo.co.uk>
 To: Kristofer Munsterhjelm <km_elmet at t-online.de>; VoteFair <electionmethods at votefair.org>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com> 
 Sent: Monday, 5 June 2017, 18:19
 Subject: Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?

By the way, a sensible Hare version of proportionality for solid coalitions would be that for a faction to be guaranteed s seats, then they should need s - 0.5 Hare quotas (or just over), rather than s Hare quotas. In the single-winner case, this would translate to 50% of the vote. This is what Sainte-Laguë guarantees.

      From: Toby Pereira <tdp201b at yahoo.co.uk>
 To: Kristofer Munsterhjelm <km_elmet at t-online.de>; VoteFair <electionmethods at votefair.org>; "election-methods at lists.electorama.com" <election-methods at lists.electorama.com> 
 Sent: Monday, 5 June 2017, 18:09
 Subject: Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?

As I was saying before, while Droop proportionality has gained a lot of currency as a criterion, it's just a special case of proportionality for solid coalitions. We could just as easily talk about Hare proportionality. For example, the Sainte-Laguë party list method doesn't obey Droop proportionality, but is seen as more mathematically proportional than D'Hondt, which does obey it. But Sainte-Laguë does obey proportionality for solid coalitions more generally. The point is that Droop proportionality itself is not a deal breaker for a method, and I find it slightly overused.

      From: Kristofer Munsterhjelm <km_elmet at t-online.de>

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.

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