<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:10pt"><div><span></span></div><div>I sort of skimmed over this in the initial post, but where methods fail "independence of commonly rated candidates", it seems that they can also fail proportionality in a more obvious way. In my example in the message quoted below, you might not consider it to be a failure of proportionality. However, partial agreement between factions does lead to a violation of proportionality when there is a third unconnected faction. For example:</div><div><br></div><div>20 voters: A1, A2, A3</div><div>10 voters: A1, A2, A4</div><div>30 voters: B1, B2, B3, B4</div><div><br></div><div>My method and I think any STV method would elect A1, A2, A3, B1, B2, B3. But Reweighted Range Voting <a
href="http://www.rangevoting.org/RRV.html"><font>http://www.rangevoting.org/RRV.html</font></a>, Forest Simmons's proportional approval voting and Thorvald N Thiele's version <a href="http://wiki.electorama.com/wiki/Proportional_approval_voting">http://wiki.electorama.com/wiki/Proportional_approval_voting</a> (which all have very similar implementation) all elect A1, A2, B1, B2, B3, B4 giving the B faction 4 candidates instead of the more proportional 3. I would argue that because of this, they are not fully proportional systems.</div><div style="color: rgb(0, 0, 255); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13.33px; font-style: normal; background-color: transparent;"><br></div><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13.33px; font-style: normal; background-color: transparent;"><font color="#000000"><font
color="#000000">Had the</font> two A factions been in complete agreement or complete disagreement, then they would have had three candidates elected between them. It's the partial agreement that counts against them.</font></div><div><br></div><div><br><blockquote 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 style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 10pt;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 12pt;"> <div dir="ltr"> <div style="margin: 5px 0px; padding: 0px; border: 1px solid rgb(204, 204, 204); border-image: none; height: 0px; line-height: 0; font-size: 0px;" contenteditable="false" readonly="true"></div> <font face="Arial" size="2"> <b><span style="font-weight: bold;">From:</span></b> Toby Pereira
<tdp201b@yahoo.co.uk><br> <b><span style="font-weight: bold;">To:</span></b> "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Sent:</span></b> Saturday, 31 May 2014, 17:32<br> <b><span style="font-weight: bold;">Subject:</span></b> [EM] Proportional Approval System<br> </font> </div> <div><br><div id="yiv9671839832"><div><div style="color: rgb(0, 0, 0); font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 10pt; background-color: rgb(255, 255, 255);"><div dir="ltr"><div><br></div><div><br></div><div>But this also works where there are commonly rated candidates. For example:</div><div><br></div><div>6 to elect</div><div><div><br></div><div>20 voters: A, B, C, D, E, F</div><div>10 voters: A, B, C, G, H, I</div><div><br></div></div><div>Reweighted Range Voting <a href="http://www.rangevoting.org/RRV.html" target="_blank"
rel="nofollow">http://www.rangevoting.org/RRV.html</a> would elect A, B, C, D, E, F on the basis that 20 voters get 3 candidates and 10 voters get 3, making it "proportional". But I would argue it's best to ignore
candidates approved by all when considering who else to elect. In this case the 20 ABCDEF voters would all have a score of 3 * 1/30 + 3 * 1/20 = 1/4. The 10 ABCGHI voters would score 3 * 1/30 = 1/10.<br></div></div></div></div></div></div> </div> </div> </blockquote><div></div> </div></body></html>