From: Toby Pereira <tdp201b@yahoo.co.uk>

  From: Toby Pereira <tdp201b@yahoo.co.uk>

  From: Toby Pereira <tdp201b@yahoo.co.uk>

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

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@yahoo.co.uk> To: Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@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@yahoo.co.uk> To: Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@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@yahoo.co.uk> To: Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@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@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.

I introduced a Harmonic Mean quota as the happy medium of the Hare and Droop quotas, because both have democratic deficiencies. It is explained in my book Scientific Method of Elections, as is my generalisation of STV: Binomial STV (free from Smashwords and in the pdf Archive). from Richard Lung. On 06/06/2017 11:43, 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. > > 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@yahoo.co.uk> > *To:* Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair > <electionmethods@votefair.org>; > "election-methods@lists.electorama.com" > <election-methods@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@yahoo.co.uk> > *To:* Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair > <electionmethods@votefair.org>; > "election-methods@lists.electorama.com" > <election-methods@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@yahoo.co.uk> > *To:* Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair > <electionmethods@votefair.org>; > "election-methods@lists.electorama.com" > <election-methods@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@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. > > > > > > > > > > > > ---- > Election-Methods mailing list - seehttp://electorama.com/em for list info -- Richard Lung. http://www.voting.ukscientists.com Democracy Science series 3 free e-books in pdf: https://plus.google.com/106191200795605365085 E-books in epub format: https://www.smashwords.com/profile/view/democracyscience

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.