<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:16px"><div id="yui_3_16_0_1_1412765264319_24550" dir="ltr"><font id="yui_3_16_0_1_1412765264319_24555" style="font-size: 13px;">From: Kathy Dopp <</font><a id="yui_3_16_0_1_1412765264319_24519" href="mailto:kathy.dopp@gmail.com"><font id="yui_3_16_0_1_1412765264319_24549" style="font-size: 13px;">kathy.dopp@gmail.com</font></a><font style="font-size: 13px;"><font id="yui_3_16_0_1_1412765264319_24556">><br></font><font id="yui_3_16_0_1_1412765264319_24547"> </font></font></div><div id="yui_3_16_0_1_1412765264319_24558"><font id="yui_3_16_0_1_1412765264319_24551" style="font-size: 13px;">>> My<br>>> system, for example, uses squared rather than absolute deviation (and uses a<br>>> different measure of deviation anyway) and it gives the results that I<br>>> wanted it to when I tested it, including stable results for the largest two<br>>> factions when the size of the third tiny faction changes, and the three-way<br>>> tie from the other example. It doesn't work by ignoring or eliminating<br>>> smaller factions;</font></div><div id="yui_3_16_0_1_1412765264319_24559"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24560"><font id="yui_3_16_0_1_1412765264319_24552" style="font-size: 13px;">>Neither does mine (in case you are implying such) Some party list<br>>systems do work that way however.</font></div><div id="yui_3_16_0_1_1412765264319_24561"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24562" dir="ltr"><font id="yui_3_16_0_1_1412765264319_25749" style="font-size: 13px;">I wasn't implying that but you suggested in one of your posts that it might be desirable. I was just saying that my system deals with it "naturally" - i.e. without manually taking out factions.</font></div><div id="yui_3_16_0_1_1412765264319_24587"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24598"><font id="yui_3_16_0_1_1412765264319_24563" style="font-size: 13px;">>> And I'm still unsure how to translate your method into approval voting with<br>>> overlapping factions.</font></div><div id="yui_3_16_0_1_1412765264319_24599"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24602"><font id="yui_3_16_0_1_1412765264319_24553" style="font-size: 13px;">>It works exactly the same way with overlapping candidate support in<br>>different factions. (i.e. v_i and s_i have exactly the same meanings,<br>>the number of voters in the group and the number of winning candidates<br>>each group contributes to electing.</font></div><div id="yui_3_16_0_1_1412765264319_24603"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24604" dir="ltr"><font id="yui_3_16_0_1_1412765264319_25744" style="font-size: 13px;">But what I mean is that if a large faction (with say 50% of all voters) is divided into two (say 25% each) because of a single controversial candidate who appears on half of that faction's ballots but not the other half, then if that faction receives half the candidates (and the one controversial candidate is not elected), then it will be measured as unproportional because each faction will have each contributed to 50% of the candidates but will only be 25% of the electorate each.</font></div><div id="yui_3_16_0_1_1412765264319_24601"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24640"><font id="yui_3_16_0_1_1412765264319_25745" style="font-size: 13px;"><font id="yui_3_16_0_1_1412765264319_24588">>What is the logic of using squared rather than absolute deviation? and<br>>are you also selecting the slate of candidates minimizing your </font><font id="yui_3_16_0_1_1412765264319_24613">formula?</font></font></div><div id="yui_3_16_0_1_1412765264319_24641"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_24642" dir="ltr"><font id="yui_3_16_0_1_1412765264319_25746" style="font-size: 13px;">Squared deviation gave better and more consistent results when I tried it. I always come armed with election scenarios where I have an intended result, and I see if the method being tested gives the intended result. My method with squared deviation gave every result I wanted it to. Absolute deviation didn't.</font></div><div id="yui_3_16_0_1_1412765264319_25767" dir="ltr"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_25769" dir="ltr"><font id="yui_3_16_0_1_1412765264319_25768" style="font-size: 13px;">And yes, in my method the winning set would be the one with the lowest sum of the squared deviations. Well, not necessarily, because if candidates could be elected sequentially, which could give a different result.</font></div><font id="yui_3_16_0_1_1412765264319_25748" style="font-size: 13px;"><div id="yui_3_16_0_1_1412765264319_25747"><font style="font-size: 13px;"></font><br></div><div id="yui_3_16_0_1_1412765264319_25766" dir="ltr">Toby</div><div><font style="font-size: 13px;"><br></font></div></font><div id="yui_3_16_0_1_1412765264319_24616"><br></div><div id="yui_3_16_0_1_1412765264319_24618"><br></div></div></body></html>