<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div><span></span></div><div id="yui_3_16_0_1_1412332069246_2863" dir="ltr">Kathy, would you be able to give some examples of this in action to flesh it out a bit? I'm a bit unsure about how it would work in practice. For example, if 1000 people vote for the candidates A, B, C, D, E and one person votes for A, B, C, D, F, then that one person is a very small faction. But If A, B, C, D are all elected then this very small faction (one person) has contributed to the election of four candidates, so I think it would cause your measure to rate it as quite unproportional. But in reality the one person is very closely related to the 1000 so shouldn't be seen as an entirely separate faction. We could also imagine a hypothetical case where although, broadly speaking, the voters are in factions, no two voters have identical ballots.</div><div dir="ltr"><br></div><div dir="ltr">Toby</div><div id="yui_3_16_0_1_1412332069246_2854"><br> </div><blockquote id="yui_3_16_0_1_1412332069246_2851" style="padding-left: 5px; margin-top: 5px; margin-left: 5px; border-left-color: rgb(16, 16, 255); border-left-width: 2px; border-left-style: solid;"> <div id="yui_3_16_0_1_1412332069246_2850" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px;"> <div id="yui_3_16_0_1_1412332069246_2849" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 12px;"> <div id="yui_3_16_0_1_1412332069246_2848" dir="ltr"> <hr size="1" id="yui_3_16_0_1_1412332069246_2847"> <font id="yui_3_16_0_1_1412332069246_2855" face="Arial" size="2"> <b><span style="font-weight: bold;">From:</span></b> Kathy Dopp <kathy.dopp@gmail.com><br> <b><span style="font-weight: bold;">To:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de> <br><b><span style="font-weight: bold;">Cc:</span></b> Toby Pereira <tdp201b@yahoo.co.uk>; EM <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Sent:</span></b> Thursday, 2 October 2014, 18:31<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] General PR question (from Andy Jennings in 2011)<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1412332069246_2856"><br>OK. Here's the formula that will *always* work to evaluate how<br clear="none">proportional fair any election result is, given any set of voter<br clear="none">groups and the combination of approval votes each group casts:<br clear="none"><br clear="none">Sum(Absolute(v_i/v - s_i/s))<div class="qtdSeparateBR"><br><br></div><div class="yqt9330229420" id="yqtfd18296"><br clear="none">or</div><br clear="none"><br clear="none">Sum(|v_i/v - s_i/s|)<br clear="none"><br clear="none">Where v_i and s_i are, respectively the number of voters in group i<br clear="none">and the winning candidates group i voted for (for any group voting for<br clear="none">the same combination of voters)<br clear="none"><br clear="none">and where v is the total number of voters and s is the total number of seats.<br clear="none"><br clear="none">Thus, for an approval vote election, one fairly simple way to find the<br clear="none">most proportionately fair set of winning candidates would be to find<br clear="none">the set of candidates who minimize this sum of absolute values of the<br clear="none">differences between the proportion of the voters in each voting block<br clear="none">that votes for the same combination of candidates out of all voters,<br clear="none">and the proportion of seats that this group contributes to electing.<br clear="none"><br clear="none"><br clear="none">I am convinced this method of counting approval ballots will never<br clear="none">fail to assign the most proportional outcomes to select the winning<br clear="none">set of candidates. If there are more than one set of candidates with<br clear="none">the same minimum sum, perhaps toss a coin.<br clear="none"><br clear="none">I actually like this proportional voting method very much because it<br clear="none">strictly adheres to finding the most proportionately fair set of<br clear="none">winning candidates, the vote tallies are easily precinct summable and<br clear="none">auditable, the vote casting method is easy and gives voters more<br clear="none">choice and flexibility to express themselves, and the method is fairly<br clear="none">(equally) counted for all voter groups. However, perhaps the summing<br clear="none">method with its proportions and differences in tallying the votes of<br clear="none">all voter groups voting for the same candidates is a little too<br clear="none">complex for some voters to comprehend.<div class="yqt9330229420" id="yqtfd82871"><br clear="none"></div><br><br></div> </div> </div> </blockquote> </div></body></html>