<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_1_1496733772650_5418" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5417">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.</span></div><div id="yui_3_16_0_1_1496733772650_5624" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5489" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5631">For example, let's say there are five seats.</span></div><div id="yui_3_16_0_1_1496733772650_5623" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5622" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5621">To guarantee one seat, a party would need 0 Hare quotas and one Droop, so 1/6 of the total vote.</span></div><div id="yui_3_16_0_1_1496733772650_5490" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5620" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5619">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</span></div><div id="yui_3_16_0_1_1496733772650_5618" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5492" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5491">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.</span></div><div id="yui_3_16_0_1_1496733772650_5526" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5527" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5528">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.</span></div><div id="yui_3_16_0_1_1496733772650_5642" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5680" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5679">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.</span></div><div dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1496733772650_5797" dir="ltr"><span id="yui_3_16_0_1_1496733772650_5796">I think this is correct now. According to the Wikipedia <a id="yui_3_16_0_1_1496733772650_5795" href="https://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions">https://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions</a> 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.</span></div><div id="yui_3_16_0_1_1496733772650_5807"><br></div><div id="yui_3_16_0_1_1496733772650_5840"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_1_1496733772650_5410"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_1_1496733772650_5350" style="display: block;"> <div id="yui_3_16_0_1_1496733772650_5349" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yui_3_16_0_1_1496733772650_5348" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yui_3_16_0_1_1496733772650_5347" dir="ltr"> <font id="yui_3_16_0_1_1496733772650_5346" face="Arial" size="2"> <hr size="1" id="yui_3_16_0_1_1496733772650_5409"> <b id="yui_3_16_0_1_1496733772650_5536"><span id="yui_3_16_0_1_1496733772650_5535" style="font-weight: bold;">From:</span></b> Toby Pereira <tdp201b@yahoo.co.uk><br> <b id="yui_3_16_0_1_1496733772650_5538"><span id="yui_3_16_0_1_1496733772650_5537" style="font-weight: bold;">To:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b id="yui_3_16_0_1_1496733772650_5494"><span id="yui_3_16_0_1_1496733772650_5493" style="font-weight: bold;">Sent:</span></b> Monday, 5 June 2017, 18:23<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1496733772650_5351"><br><div id="yiv7522587144"><div id="yui_3_16_0_1_1496733772650_5407"><div id="yui_3_16_0_1_1496733772650_5406" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px; background-color: rgb(255, 255, 255);"><div id="yui_3_16_0_1_1496733772650_5408"><span id="yui_3_16_0_1_1496733772650_5419">I think that's wrong actually. Forget that last post!</span></div><div class="yiv7522587144qtdSeparateBR" id="yiv7522587144yui_3_16_0_1_1496653143426_13715"><br clear="none"><br clear="none"></div><div class="yiv7522587144yqt3344238213" id="yiv7522587144yqt92422"><div class="yiv7522587144yahoo_quoted" id="yiv7522587144yui_3_16_0_1_1496653143426_13709" style="display: block;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_13708" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_13707" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_13706" dir="ltr"> <font id="yiv7522587144yui_3_16_0_1_1496653143426_13714" face="Arial" size="2"> </font><hr size="1" id="yiv7522587144yui_3_16_0_1_1496653143426_13713"> <b><span style="font-weight: bold;">From:</span></b> Toby Pereira <tdp201b@yahoo.co.uk><br clear="none"> <b><span style="font-weight: bold;">To:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br clear="none"> <b><span style="font-weight: bold;">Sent:</span></b> Monday, 5 June 2017, 18:19<br clear="none"> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?<br clear="none"> </div> <div class="yiv7522587144y_msg_container" id="yiv7522587144yui_3_16_0_1_1496653143426_13716"><br clear="none"><div id="yiv7522587144"><div id="yiv7522587144yui_3_16_0_1_1496653143426_13718"><div id="yiv7522587144yui_3_16_0_1_1496653143426_13717" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px; background-color: rgb(255, 255, 255);"><div id="yiv7522587144yui_3_16_0_1_1496653143426_12079" dir="ltr"><span id="yiv7522587144yui_3_16_0_1_1496653143426_12078">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.</span></div><div class="yiv7522587144qtdSeparateBR" id="yiv7522587144yui_3_16_0_1_1496653143426_12071"><br clear="none"><br clear="none"></div><div class="yiv7522587144yqt9110754160" id="yiv7522587144yqt52335"><div class="yiv7522587144yahoo_quoted" id="yiv7522587144yui_3_16_0_1_1496653143426_12067" style="display: block;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_12066" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_12065" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_12064" dir="ltr"> <font id="yiv7522587144yui_3_16_0_1_1496653143426_12063" face="Arial" size="2"> </font><hr size="1"> <b><span style="font-weight: bold;">From:</span></b> Toby Pereira <tdp201b@yahoo.co.uk><br clear="none"> <b><span style="font-weight: bold;">To:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de>; VoteFair <electionmethods@votefair.org>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br clear="none"> <b><span style="font-weight: bold;">Sent:</span></b> Monday, 5 June 2017, 18:09<br clear="none"> <b id="yiv7522587144yui_3_16_0_1_1496653143426_13720"><span id="yiv7522587144yui_3_16_0_1_1496653143426_13719" style="font-weight: bold;">Subject:</span></b> Re: [EM] Resume: Proportional multi-winner ranked voting methods - guidelines?<br clear="none"> </div> <div class="yiv7522587144y_msg_container" id="yiv7522587144yui_3_16_0_1_1496653143426_12123"><br clear="none"><div id="yiv7522587144"><div id="yiv7522587144yui_3_16_0_1_1496653143426_12125"><div id="yiv7522587144yui_3_16_0_1_1496653143426_12124" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px; background-color: rgb(255, 255, 255);"><div><span></span></div><div class="yiv7522587144qtdSeparateBR" id="yiv7522587144yui_3_16_0_1_1496653143426_10847" dir="ltr">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.<br clear="none"><br clear="none"></div><div class="yiv7522587144yahoo_quoted" id="yiv7522587144yui_3_16_0_1_1496653143426_10836" style="display: block;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_10835" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_10834" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yiv7522587144yui_3_16_0_1_1496653143426_10833" dir="ltr"> <font id="yiv7522587144yui_3_16_0_1_1496653143426_10832" face="Arial" size="2"> </font><div class="yiv7522587144yqt4964028973" id="yiv7522587144yqtfd88723"><hr size="1" id="yiv7522587144yui_3_16_0_1_1496653143426_10846"> <b><span style="font-weight: bold;">From:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de><br clear="none"> <br id="yiv7522587144yui_3_16_0_1_1496653143426_10844" clear="none"><br clear="none">Perhaps Droop proportionality isn't the exact proportionality measure <br clear="none">one would want - for instance, for my Bucklin methods, I've tried to <br clear="none">base them on divisor methods rather than on hard quotas - but I think <br clear="none">the concept that "some voters who broadly agree on a group of candidates <br clear="none">should see one of them elected" is a good one. That is, that a group of <br clear="none">voters can have "their" seat without having to agree on a strategy.</div></div><div class="yiv7522587144yqt4964028973" id="yiv7522587144yqtfd64707"><div class="yiv7522587144y_msg_container" id="yiv7522587144yui_3_16_0_1_1496653143426_10842"><div id="yiv7522587144yui_3_16_0_1_1496653143426_10843" dir="ltr"><div class="yiv7522587144yqt6418950328" id="yiv7522587144yqtfd33530"><br clear="none"></div></div><br id="yiv7522587144yui_3_16_0_1_1496653143426_10845" clear="none"><br clear="none"></div> </div></div><div class="yiv7522587144yqt4964028973" id="yiv7522587144yqtfd23278"> </div></div><div class="yiv7522587144yqt4964028973" id="yiv7522587144yqtfd63573"> </div></div></div></div></div><br clear="none"><br clear="none"></div> </div> </div> </div></div></div></div></div><br clear="none"><br clear="none"></div> </div> </div> </div></div></div></div></div><br><br></div> </div> </div> </div></div></body></html>